Document:

<PAGE>

                                                                    EXHIBIT 10.3

                          SECOND AMENDED AND RESTATED

                            OPERATING AGREEMENT OF

                      INSIGHT COMMUNICATIONS MIDWEST, LLC

                                  DATED AS OF

                              JANUARY 5, 2001
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                                       TABLE OF CONTENTS                                       Page
<S>                                                                                            <C>
ARTICLE 1      DEFINITIONS....................................................................    1

        1.1    Terms Defined in this Section..................................................    1

        1.2    Terms Defined Elsewhere in this Agreement......................................    3

        1.3    Terms Generally................................................................    3

ARTICLE 2      FORMATION AND PURPOSE..........................................................    4

        2.1    Formation......................................................................    4

        2.2    Name...........................................................................    4

        2.3    Principal and Registered Office................................................    4

        2.4    Term...........................................................................    5

        2.5    Purposes of Company............................................................    5

        2.6    Certificate....................................................................    6

        2.7    Address of the Member..........................................................    6

        2.8    Foreign Qualification..........................................................    6

ARTICLE 3      COMPANY CAPITAL................................................................    7

        3.1    Contributions at Closing.......................................................    7

        3.2    Additional Capital Contributions...............................................    7

        3.3    Return of Contributions........................................................    7

ARTICLE 4      DISTRIBUTIONS; ALLOCATIONS OF PROFIT AND LOSS..................................    7

        4.1    Distributions of Cash..........................................................    7

        4.2    Allocations of Net Profit and Net Loss.........................................    7

ARTICLE 5      AUTHORITY OF THE MEMBER; OTHER MATTERS AFFECTING MEMBER........................    8

        5.1    Authority of Member............................................................    8

        5.2    Limited Liability..............................................................    8

        5.3    Return of Distributions of Capital.............................................    8

ARTICLE 6      TRANSFER OF MEMBERSHIP INTERESTS...............................................    8

        6.1    Transferees....................................................................    8

        6.2    Other Consents and Requirements................................................    9

        6.3    Assignment Not In Compliance...................................................    9

        6.4    Pledge of Membership Interest..................................................    9

ARTICLE 7      DISSOLUTION AND LIQUIDATION OF COMPANY.........................................   10

        7.1    Events of Dissolution..........................................................   10

        7.2    Liquidation....................................................................   10
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<TABLE>
<S>                                                                                              <C>
ARTICLE 8      INDEMNIFICATION................................................................   11

        8.1    General........................................................................   11

        8.2    Exculpation....................................................................   11

        8.3    Persons Entitled to Indemnity..................................................   11

        8.4    Procedure Agreements...........................................................   12

ARTICLE 9      BOOKS, RECORDS, ACCOUNTING, AND REPORTS........................................   12

        9.1    Books and Records..............................................................   12

        9.2    Other Filings..................................................................   12

ARTICLE 10     AMENDMENTS AND WAIVERS.........................................................   12

        10.1   Amendments to Operating Agreement..............................................   12

        10.2   Waivers........................................................................   13

ARTICLE 11     MISCELLANEOUS..................................................................   13

        11.1   General........................................................................   13

        11.2   Notices, Etc...................................................................   13

        11.3   No Third-Party Beneficiaries...................................................   13

        11.4   Headings.......................................................................   13
</TABLE>

                                      -ii-
<PAGE>

                          SECOND AMENDED AND RESTATED
                              OPERATING AGREEMENT
                                      OF
                      INSIGHT COMMUNICATIONS MIDWEST, LLC

     THIS SECOND AMENDED AND RESTATED OPERATING AGREEMENT OF INSIGHT
COMMUNICATIONS MIDWEST, LLC (formerly known as Insight Communications of
Indiana, LLC) is made and entered into as of January 5, 2001, by INSIGHT
COMMUNICATIONS MIDWEST, LLC, a Delaware limited liability company (the
"Company"), and INSIGHT MIDWEST HOLDINGS, LLC, a Delaware limited liability
company ("Holdings"), the sole member of the Company.

                                   RECITALS
                                   --------

     A.   The Company (formerly known as Insight Communications of Indiana, LLC)
was formed on May 1, 1998 pursuant to the Act and, concurrently with the
execution of this Agreement, has changed its name to Insight Communications
Midwest, LLC by filing an amendment to the Certificate with the office of the
Secretary of State of the State of Delaware.

     B.   Pursuant to the Contribution Agreement, immediately prior to the
closing under the Contribution Agreement, Insight Midwest has contributed its
100% limited liability company interest in the Company to Holdings with the
result that Holdings is, effective immediately prior to the closing under the
Contribution Agreement, the sole member of the Company.

     C.   Effective immediately following the closing under the Contribution
Agreement, the parties hereto desire to amend and restate the Amended and
Restated Operating Agreement of the Company dated as of October 1, 1999 in its
entirety as set forth herein in order to reflect certain changes and, among
other things, to reflect that Holdings is the new sole member of the Company and
that the name of the Company has been changed.

     NOW, THEREFORE, in consideration of the mutual covenants contained herein
and other good and valuable consideration, the receipt of which is hereby
acknowledged, the parties hereto, intending to be legally bound, agree as
follows:

                                   ARTICLE 1

                                  DEFINITIONS

     1.1  Terms Defined in this Section.
          -----------------------------

     For purposes of this Agreement, the following terms shall have the
following meanings (all terms used in this Agreement that are not defined in
this Section 1.1 shall have the meanings set forth elsewhere in this Agreement
as indicated in Section 1.2, except as otherwise provided in this Agreement):
<PAGE>

     "Act" means the Delaware Limited Liability Company Act, as it may be
amended from time to time.

     "Agreement" means this Agreement, as it may be amended from time to time.

     "Business Day" means any day (other than a day that is a Saturday or
Sunday) on which banks are permitted to be open for business in the State of New
York.

     "Capital Account" means an individual capital account to be maintained for
the Member the balance of which shall equal the amount of Capital Contributions
made or deemed made by the Member plus allocations to the Member of net profit
pursuant to Section 4.2 decreased by the amount of cash and the fair market
value of property distributed to the Member by the Company and allocations to
the Member of net loss pursuant to Section 4.2.

     "Capital Contribution" means, with respect to a Member, the amount of money
and the net fair market value of property contributed to the Company pursuant to
this Agreement.

     "Certificate" means the certificate of formation filed with respect to the
Company pursuant to the Act.

     "Code" means the Internal Revenue Code of 1986, as amended from time to
time, and any subsequent federal law of similar import, and, to the extent
applicable, the Treasury Regulations.

     "Contribution Agreement" means that certain Asset Contribution Agreement
dated as of August 15, 2000, by and among TCI of Indiana Holdings, LLC and
certain of its affiliates, Insight Communications Company, L.P., and Insight
Midwest, as it has been or may be amended from time to time.

     "Fiscal Year" means the fiscal year of the Company, which shall be the
calendar year.

     "Insight Midwest" means Insight Midwest, L.P., a Delaware limited
partnership.

     "Insight Midwest Partnership Agreement" means the Amended and Restated
Limited Partnership Agreement of Insight Midwest dated as of January 5, 2001,
as it may be amended from time to time.

     "Management Agreement" means the Amended and Restated Management Agreement
dated as of October 1, 1999 between the Company and Manager, as it may be
amended from time to time.

     "Manager" means Insight Communications Company, L.P.

     "Member" means Holdings in its capacity as the Member of the Company or any
other Person that succeeds to its Membership Interest and is admitted as a
Member in accordance with the provisions of this Agreement, and any additional
Person that is admitted as a Member in accordance with the provisions of this
Agreement.

                                      -2-
<PAGE>

     "Membership Interest" means the entire ownership interest of the Member in
the Company at any particular time, including all of its rights and obligations
hereunder and under the Act.

     "Person" means an individual, partnership, joint venture, association,
corporation, trust, estate, limited liability company, limited liability
partnership, or any other legal entity.

     "Subsidiary" means, at any time, any Person that is controlled by the
Company at such time.

     "Transferee" means any Person that acquires a Membership Interest from a
Member in accordance with the provisions of this Agreement.

     1.2  Terms Defined Elsewhere in this Agreement.
          -----------------------------------------

     For purposes of this Agreement, the following terms have the meanings set
forth in the sections indicated:

     Term                                           Section
     ----                                           -------

     Company                                        Preamble

     Contribution Assets                            Section 3.1

     Holdings                                       Preamble

     Indemnified Persons                            Section 8.1

     Transfer                                       Section 6.1(a)

     1.3  Terms Generally.
          ---------------

     The definitions in Section 1.1 and elsewhere in this Agreement shall apply
equally to both the singular and plural forms of the terms defined. Whenever the
context requires, any pronoun includes the corresponding masculine, feminine,
and neuter forms. The words "include," "includes," and "including" are not
limiting. Any reference in this Agreement to a "day" or number of "days"
(without the explicit qualification of "Business") shall be interpreted as a
reference to a calendar day or number of calendar days. If any action or notice
is to be taken or given on or by a particular calendar day, and such calendar
day is not a Business Day, then such action or notice shall be deferred until,
or may be taken or given on, the next Business Day.

                                      -3-
<PAGE>

                                   ARTICLE 2

                             FORMATION AND PURPOSE

     2.1  Formation.
          ---------

     The Company was formed on May 1, 1998 as a limited liability company
pursuant to the Act. The parties agree to continue the Company as a limited
liability company pursuant to the provisions of the Act. The rights and
liabilities of the Member shall be determined pursuant to the Act and this
Agreement. To the extent that the rights or obligations of the Member are
different by reason of any provision of this Agreement than they would be in the
absence of such provision, this Agreement shall, to the extent permitted by the
Act, control.

     2.2  Name.
          ----

          (a)  The name of the Company is Insight Communications Midwest, LLC.
Except as provided in Section 2.2(b), the business of the Company may be
conducted under that name or, upon compliance with applicable laws, any other
name that the Member deems appropriate or advisable. The Company shall file any
assumed name certificates and similar filings, and any amendments thereto, that
the Member considers appropriate or advisable. Such names and any trade or
service names, marks, emblems or logos used by the Company shall be exclusive
property of the Company and no Person shall have any right to use, and the
Member agrees not to use, any of said names, marks, emblems or logos other than
on behalf of the Company (other than any of the foregoing that incorporates the
name "Insight" or any variant thereof, which shall remain the exclusive property
of Insight Communications Company, L.P. and its affiliates and may be used by
Insight Communications Company, L.P. and its affiliates without limitation).

          (b)  The Company shall not conduct business under the name "Tele-
Communications, Inc.," "TCI," "AT&T" or any variation thereof without the
approval of TCI of Indiana Holdings, LLC. The parties agree that
"Communications" is not a variation of "Tele-Communications, Inc." for purposes
of this Section 2.2(b).

     2.3  Principal and Registered Office.
          -------------------------------

     The office required to be maintained by the Company in the State of
Delaware pursuant to Section 18-104 of the Act shall initially be located at
1209 Orange Street, Wilmington, New Castle County, Delaware 19801. The resident
agent of the Company pursuant to Section 18-104 of the Act shall initially be
The Corporation Trust Company. The Company may, upon compliance with the
applicable provisions of the Act, change its principal office or resident agent
from time to time in the discretion of the Member. The principal office of the
Company shall be located at 810 7th Avenue, New York, New York 10019, or at such
other place as the Member shall from time to time designate. The Company may
conduct business at such additional places as the Member shall deem advisable.

                                      -4-
<PAGE>

     2.4  Term.
          ----

     The term of the Company commenced when the Certificate was filed with the
Secretary of State of Delaware, and shall continue until October 1, 2011, unless
sooner terminated as provided in this Agreement.

     2.5  Purposes of Company.
          -------------------

     The purposes of the Company are:

          (a)  to engage in the business, directly or indirectly through
interests in one or more Subsidiaries, of acquiring, developing, owning,
operating, managing, and selling cable television systems in the State of
Georgia, State of Indiana, State of Illinois, and in the Commonwealth of
Kentucky;

          (b)  to acquire, develop, own, operate, manage, and sell additional
cable television systems in the State of Georgia, State of Indiana, State of
Illinois, and in the Commonwealth of Kentucky and such other States as the
Member may determine;

          (c)  to acquire, develop, own, operate, manage, and sell, or invest
in, businesses related to and ancillary to the ownership and operation of the
cable television systems referred to above (including, but not limited to, high
speed data service, internet access, telephony services and other telephony-
related investments or businesses, and video wireless services and wireless
communications services and other wireless-related investments or businesses but
not including multipoint distribution systems ("MDS"), multichannel multipoint
distribution systems ("MMDS"), direct-to-home satellite systems ("DTH") or
Internet Backbone Services (as defined in the Insight Midwest Partnership
Agreement), it being agreed that the use of IP technology to provide telephone,
fax, video, video conferencing, telecommuting, virtual private networks,
security and energy management services to subscribers of the Company's cable
television systems does not constitute engaging in an Internet Backbone Service
and, subject to Section 16.1(b) of the Insight Midwest Partnership Agreement, is
within the purposes of the Company;

          (d)  to conduct other businesses as determined by the Member;

          (e)  in connection with the businesses described in Section 2.5(a)-
(d), to possess, transfer, mortgage, pledge, or otherwise deal in, and to
exercise all rights, powers, privileges, and other incidents of ownership or
possession with respect to securities or other assets held or owned by the
Company, and to hold securities or assets in the name of a nominee or nominees;

          (f)  in connection with the businesses described in Section 2.5(a)-
(d), to borrow or raise money, and from time to time to issue, accept, endorse,
and execute promissory notes, loan agreements, options, stock purchase
agreements, contracts, documents, checks, drafts, bills of exchange, warrants,
bonds, debentures, and other negotiable or non-negotiable instruments and
evidences of indebtedness, and to secure the payment of any thereof and of the
interest thereon by mortgage upon or pledge, conveyance, or assignment in trust
of, the whole or any part of the property of the Company whether at the time
owned or thereafter acquired and to guarantee the

                                      -5-
<PAGE>

obligations of others and to sell, pledge, or otherwise dispose of such bonds or
other obligations of the Company for its purposes;

          (g)  in connection with the businesses described in Section 2.5(a)-
(d), to guarantee the obligations of others in connection with the purchase or
acquisition by the Company of securities or assets;

          (h)  to maintain an office or offices in such place or places as the
Member shall determine and in connection therewith to rent or acquire office
space, engage personnel, and do such other acts and things as may be necessary
or advisable in connection with the maintenance of such office, and on behalf of
and in the name of the Company to pay and incur reasonable expenses and
obligations for legal, accounting, investment advisory, consultative and
custodial services, and other reasonable expenses including taxes, travel,
insurance, rent, supplies, interest, salaries and wages of employees, and all
other reasonable costs and expenses incident to the operation of the Company;

          (i)  to form and own one or more corporations, trusts, partnerships or
other entities (but no entity so formed or owned, while it is a Subsidiary, may
do what the Company is prohibited by this Agreement from doing); and

          (j)  to own, lease, or otherwise acquire any and all assets and
services related to the foregoing purposes and to engage in such other
activities related either directly or indirectly to the foregoing purposes as
may be necessary, advisable, or appropriate, in the opinion of the Member, for
the promotion or conduct of the business of the Company.

     2.6  Certificate.
          -----------

     The Member shall cause any amendment to the Certificate required under the
Act to be filed or recorded with the Secretary of State of Delaware and in any
other public office where filing or recording is required or is deemed by the
Member to be advisable.

     2.7  Address of the Member.
          ---------------------

     The address of the Member is 810 7th Avenue, New York, New York 10019,
Attention: Michael S. Willner, Facsimile: (917) 286-2301.

     2.8  Foreign Qualification.
          ---------------------

     The Member shall take all necessary actions to cause the Company to be
authorized to conduct business legally in all appropriate jurisdictions,
including registration or qualification of the Company as a foreign limited
liability company in those jurisdictions that provide for registration or
qualification and the filing of a certificate of limited liability company in
the appropriate public offices of those jurisdictions that do not provide for
registration or qualification.

                                      -6-
<PAGE>

                                   ARTICLE 3

                                COMPANY CAPITAL
                                ---------------

     3.1  Contributions at Closing.

     Pursuant to the terms of the Contribution Agreement, immediately following
the closing under the Contribution Agreement and Holdings' receipt of the assets
described in Section 3.1(b) of the Operating Agreement of Holdings dated as of
December 14, 2000 (the "Contribution Assets"), Holdings will contribute to the
Company all of the Contribution Assets.

     3.2  Additional Capital Contributions.

     The Member may make additional Capital Contributions to the Company as it
deems appropriate.

     3.3  Return of Contributions.

     The Member shall not have the right to demand a return of all or any part
of its Capital Contribution during the term of the Company, and any return of
the Capital Contribution of the Member shall be made solely from the assets of
the Company and only in accordance with the terms of this Agreement. No interest
shall be paid to the Member with respect to its Capital Contribution to the
Company.

                                   ARTICLE 4

                 DISTRIBUTIONS; ALLOCATIONS OF PROFIT AND LOSS
                 ---------------------------------------------

     4.1  Distributions of Cash.

     Distributions shall be made to the Member at the times and in the aggregate
amounts determined by the Member. Notwithstanding any other provision of this
Agreement to the contrary, no distribution shall be made that would render the
Company insolvent or which is prohibited by the Act.

     4.2  Allocations of Net Profit and Net Loss.

     Net profit and net loss for each Fiscal Year (or portion thereof) shall be
allocated to the Member.

                                      -7-
<PAGE>

                                   ARTICLE 5

                           AUTHORITY OF THE MEMBER;
                           ------------------------
                        OTHER MATTERS AFFECTING MEMBER
                        ------------------------------

     5.1  Authority of Member.
          -------------------

     The business of the Company shall be managed by the Member pursuant to the
provisions of this Agreement. The Member shall have exclusive authority and full
discretion with respect to the management of the business of the Company and the
Subsidiaries. Notwithstanding the foregoing, the Member shall not take any
action with respect to the Company or the Member's Membership Interest that
requires the consent of the limited partner of Insight Midwest pursuant to the
Insight Midwest Partnership Agreement without first obtaining such consent,
including any Transfer of its Membership Interest. The Member may delegate to
the Manager any of the powers and authority of the Member under this Agreement
and the Act to the extent delegated in the Management Agreement.

     5.2  Limited Liability.
          -----------------

     The Member shall not be bound by or personally liable for the expenses,
liabilities, or obligations of the Company. In no event shall the Member be
required to make up a deficiency in its Capital Account upon the dissolution and
termination of the Company.

     5.3  Return of Distributions of Capital.
          ----------------------------------

     The Member may, under certain circumstances, be required by law to return
to the Company, for the benefit of the Company's creditors, amounts previously
distributed. The Member shall be obligated by this Agreement to pay those
distributions to or for the account of the Company or any creditor of the
Company. Any payment returned to the Company by the Member or made directly by
the Member to a creditor of the Company shall be deemed a Capital Contribution
by the Member.

                                   ARTICLE 6

                       TRANSFER OF MEMBERSHIP INTERESTS
                       --------------------------------

     6.1  Transferees.
          -----------

          (a)  No sale, assignment, transfer or other disposition (any or all of
the foregoing, a "Transfer") of a Membership Interest will be effective nor will
any purported Transferee become a Member or otherwise be entitled to any
attributes of ownership of the Company purportedly Transferred unless such
Transfer is made in accordance with the provisions of this Article 6 and Section
5.1 of this Agreement and the transferor and Transferee have complied with the
following conditions:

               (1)  the transferor has executed and delivered to the Company a
copy of the assignment of the Membership Interest to Transferee in form and
substance satisfactory to the Company;

                                      -8-
<PAGE>

               (2)  the Transferee becomes a party to this Agreement, assumes
all of the obligations hereunder of its transferor and agrees to be bound by the
terms and conditions hereof in the same manner as the transferor.

          (b)  Upon compliance with Section 6.1(a), any Transferee shall be
substituted as a Member for, and shall enjoy the same rights and be subject to
the same obligations as, its predecessor as a Member hereunder.

          (c)  If there is a permitted Transfer of a Membership Interest under
this Agreement:

               (1)  A Transferee's percentage interest in the Company shall
equal the percentage interest transferred to it by the transferring Member; and

               (2)  A Transferee's Capital Account shall initially be equal to
the Capital Account balance transferred to it by the transferring Member.

     6.2  Other Consents and Requirements.
          -------------------------------

     Any Transfer must be in compliance with all requirements imposed by any
state securities administrator having jurisdiction over the Transfer and the
United States Securities and Exchange Commission.

     6.3  Assignment Not In Compliance.
          ----------------------------

     Any Transfer in contravention of any of the provisions of this Article 6
(whether voluntarily, involuntarily or by operation of law) shall be void and of
no effect, and shall neither bind nor be recognized by the Company.

     6.4  Pledge of Membership Interest.
          -----------------------------

     Notwithstanding Section 6.1, the Member may pledge its Membership Interest
to secure any indebtedness of the Company that is permitted under the Insight
Midwest Partnership Agreement, provided that if a secured party under any such
pledge enforces its rights against the Membership Interest of the Member, any
assignment, transfer or other disposition of the Membership Interest to such
secured party shall constitute a Transfer which is subject to Sections 6.1, 6.2
and 6.3.

                                   ARTICLE 7

                    DISSOLUTION AND LIQUIDATION OF COMPANY
                    --------------------------------------

     7.1  Events of Dissolution.
          ---------------------

     The Company shall be dissolved upon the happening of any of the following
events:

          (a)  the expiration of the term of the Company as set forth in Section
2.4;

          (b)  the sale, exchange, involuntary conversion, or other disposition
or transfer of all or substantially all of the assets of the Company;

                                      -9-
<PAGE>

          (c)  upon determination by the Member; or

          (d)  subject to any provision of this Agreement that limits or
prevents dissolution, the happening of any event that, under applicable law,
causes the dissolution of a limited liability company.

     7.2  Liquidation.
          -----------

          (a)  Upon dissolution of the Company for any reason, the Company shall
immediately commence to wind up its affairs. A reasonable period of time shall
be allowed for the orderly termination of the Company's business, discharge of
its liabilities, and distribution or liquidation of the remaining assets so as
to enable the Company to minimize the normal losses attendant to the liquidation
process.

          (b)  Liquidation of the assets of the Company shall be managed on
behalf of the Company by the Member.

          (c)  The property and assets of the Company and the proceeds from the
liquidation thereof shall be applied in the following order of priority:

               (1)  first, to payment of the debts and liabilities of the
Company, in the order of priority provided by law (including any loans by the
Member to the Company) and payment of the expenses of liquidation;

               (2)  second, to setting up of such reserves as the Member may
deem reasonably necessary for any contingent or unforeseen liabilities or
obligations of the Company or any obligation or liability not then due and
payable; provided, however, that any such reserve shall be paid over by the
Member into a Company account or a liquidating trust account established for
such purpose, to be held in such account for the purpose of disbursing such
reserves in payment of such liabilities, and, at the expiration of such holdback
period as the Member shall deem advisable, to distribute the balance thereafter
remaining in the manner hereinafter provided; and

               (3)  finally, to payment to the Member. The distributions
pursuant to this Section 7.2(c)(3) shall, to the extent possible, be made prior
to the later of the end of the Fiscal Year in which the dissolution occurs or
the ninetieth day after the date of dissolution, or such other time period which
may be permitted under Treasury Regulations Section 1.704-1(b)(2)(ii)(b).

                                      -10-
<PAGE>

                                   ARTICLE 8

                                INDEMNIFICATION
                                ---------------

     8.1  General.
          -------

     The Company shall indemnify, defend, and hold harmless the Member and its
respective members, partners, officers, directors, shareholders, employees, and
agents, and the employees, officers, and agents of the Company (all indemnified
persons being referred to as "Indemnified Persons" for purposes of this Article
8), from any liability, loss, or damage incurred by the Indemnified Person by
reason of any act performed or omitted to be performed by the Indemnified Person
in connection with the business of the Company, including costs and attorneys'
fees (which attorneys' fees may be paid as incurred) and any amounts expended in
the settlement of any claims of liability, loss, or damage; provided, however,
that, if the liability, loss, damage, or claim arises out of any action or
inaction of an Indemnified Person, indemnification under this Section 8.1 shall
not be available if the action or inaction is finally adjudicated to have
constituted fraud, gross negligence, breach of fiduciary duty (which shall not
be construed to encompass mistakes in judgment or any breach of any Indemnified
Person's duty of care that did not constitute gross negligence), or willful
misconduct by the Indemnified Person. The Company may pay for insurance covering
liability of the Indemnified Persons for negligence in the operation of the
Company's affairs.

     8.2  Exculpation.
          -----------

     No Indemnified Person shall be liable, in damages or otherwise, to the
Company or the Member for any loss that arises out of any act performed or
omitted to be performed by it or him pursuant to the authority granted by this
Agreement unless the conduct of the Indemnified Person is finally adjudicated to
have constituted fraud, gross negligence, breach of fiduciary duty (which shall
not be construed to encompass mistakes in judgment or any breach of any
Indemnified Person's duty of care that did not constitute gross negligence), or
willful misconduct by such Indemnified Person.

     8.3  Persons Entitled to Indemnity.
          -----------------------------

     Any Person who is within the definition of "Indemnified Person" at the time
of any action or inaction in connection with the business of the Company shall
be entitled to the benefits of this Article 8 as an "Indemnified Person" with
respect thereto, regardless of whether such Person continues to be within the
definition of "Indemnified Person" at the time of his or its claim for
indemnification or exculpation hereunder.

     8.4  Procedure Agreements.
          --------------------

     The Company may enter into agreements with the Member, any of the
employees, officers, and agents of the Company, any of the officers, directors,
shareholders, employees, and agents of the Member and any Indemnified Person,
setting forth procedures for implementing the indemnities provided in this
Article 8.

                                      -11-
<PAGE>

                                   ARTICLE 9

                    BOOKS, RECORDS, ACCOUNTING, AND REPORTS
                    ---------------------------------------

     9.1  Books and Records.
          -----------------

     The Company shall maintain at its principal office all of the following:

          (a)  A current list of the full name and last known business or
residence address of the Member together with the Capital Contributions and
Membership Interest of the Member;

          (b)  A copy of the Certificate, this Agreement, and any and all
amendments to either thereof, together with executed copies of any powers of
attorney pursuant to which any certificate or amendment has been executed;

          (c)  The audited financial statements of the Company for the six most
recent Fiscal Years; and

          (d)  The Company's books and records for at least the current and past
three Fiscal Years.

     9.2  Other Filings.
          -------------

     The Company, at Company expense, shall also prepare and timely file, with
appropriate federal and state regulatory and administrative bodies, all reports
required to be filed by the Company with those entities under then current
applicable laws, rules, and regulations. The reports shall be prepared on the
accounting or reporting basis required by the regulatory bodies.

                                  ARTICLE 10

                            AMENDMENTS AND WAIVERS
                            ----------------------

     10.1 Amendments to Operating Agreement.
          ---------------------------------

          (a)  Subject to Section 5.1 of this Agreement, this Agreement may be
modified or amended with the consent of the Member.

          (b)  The Company shall prepare and file any amendment to the
Certificate that may be required to be filed under the Act as a consequence of
any amendment to this Agreement.

     10.2 Waivers.
          -------

     The observance or performance of any term or provision of this Agreement
may be waived (either generally or in a particular instance, and either
retroactively or prospectively) by the party entitled to the benefits of such
term or provision.

                                      -12-
<PAGE>

                                  ARTICLE 11

                                 MISCELLANEOUS
                                 -------------

     11.1 General.
          -------

     This Agreement: (a) shall be binding on the executors, administrators,
estates, heirs, and legal successors of the Member; (b) shall be governed by and
construed in accordance with the laws of the State of Delaware, without regard
to conflicts of law principles thereunder; (c) may be executed in more than one
counterpart as of the day and year first above written; and (d) contains the
entire agreement between the parties as to the subject matter of this Agreement.
The waiver of any of the provisions, terms, or conditions contained in this
Agreement shall not be considered as a waiver of any of the other provisions,
terms, or conditions of this Agreement.

     11.2 Notices, Etc.
          ------------

     All notices and other communications required or permitted hereunder shall
be in writing and shall be deemed effectively given or delivered upon personal
delivery, confirmation of telex or telecopy, or receipt (which may be evidenced
by a return receipt if sent by registered mail), addressed to the Member or the
Company at 810 7th Avenue, New York, New York 10019, Attention: Michael S.
Willner, Facsimile: (917) 286-2301, with a copy to Attention: Insight Legal
Department, Facsimile: (917) 286-2301.

     11.3 No Third-Party Beneficiaries.
          ----------------------------

     This Agreement is not intended to, and shall not be construed to, create
any right enforceable by any Person not a party hereto, including any partner or
member of the Member or any creditor of the Company or the Member.

     11.4 Headings.
          --------

     The headings herein are included for ease of reference only and shall not
control or affect the meaning or construction of the provisions of this
Agreement.

                           [SIGNATURE PAGE FOLLOWS]

                                      -13-
<PAGE>

     IN WITNESS WHEREOF, the parties have hereunto set their hands as of the day
first heretofore mentioned.

                           INSIGHT MIDWEST HOLDINGS, LLC

                           By:    Insight Midwest, L.P., its sole member
                           By:    Insight Communications Company, L.P.,
                                  its general partner
                           By:    Insight Communications Company, Inc.,
                                  its general partner

                           By:    ______________________________________________
                           Name:  Elliot Brecher
                           Title: Senior Vice President and General Counsel

                           INSIGHT COMMUNICATIONS MIDWEST, LLC

                           By:    Insight Midwest Holdings, LLC, its sole member
                           By:    Insight Midwest, L.P., its sole member
                           By:    Insight Communications Company, L.P.,
                                  its general partner
                           By:    Insight Communications Company, Inc.,
                                  its general partner

                           By:    ______________________________________________
                           Name:  Elliot Brecher
                           Title: Senior Vice President and General Counsel

By signing below Insight Midwest acknowledges and agrees that it has withdrawn
as the sole member of the Company:

INSIGHT MIDWEST, L.P.

By:     Insight Communications Company, L.P.,
        its general partner
By:     Insight Communications Company, Inc.,
        its general partner

By:     _____________________________________________
Name:   Elliot Brecher
Title:  Senior Vice President and General Counsel<PAGE>

                                                                    EXHIBIT 10.5

                               FIRST AMENDMENT TO
                              AMENDED AND RESTATED
                              MANAGEMENT AGREEMENT

         THIS FIRST AMENDMENT TO AMENDED AND RESTATED MANAGEMENT AGREEMENT
("First Amendment") is made and entered into as of January 5, 2001 by and
between INSIGHT COMMUNICATIONS MIDWEST, LLC, a Delaware limited liability
company (the "Company") (formerly known as Insight Communications of Indiana,
LLC), and INSIGHT COMMUNICATIONS COMPANY, L.P., a Delaware limited partnership
("Insight" and, together with any permitted assigns hereunder, the "Manager").

                             PRELIMINARY STATEMENT

         Pursuant to that certain Asset Contribution Agreement dated as of
August 15, 2000, by and among TCI of Indiana Holdings, LLC ("TCI LLC") and
certain affiliates of TCI LLC, Insight, and Insight Midwest, L.P. (as amended,
the "Asset Contribution Agreement"), (i) immediately prior to the closing under
the Asset Contribution Agreement, Insight Midwest, L.P. ("Insight Midwest") has
contributed its 100% limited liability company interest in the Company to
Insight Midwest Holdings, LLC ("Holdings"), with the result that Holdings has
become the sole member of the Company, (ii) immediately following the closing
under the Asset Contribution Agreement, Insight Midwest has contributed to
Holdings the Insight Assets (excluding the Insight LLC Interest and the Insight
Central Ohio Assets), the Exchange Assets, the Sale Assets and the AT&T Assets
relating to the Insight Systems, the Exchange Systems, the Sale Systems and the
AT&T Systems, respectively (as those terms are defined in the Asset Contribution
Agreement) (collectively, such Systems and Assets, the "New Systems"), and (iii)
immediately following the transfer described in (ii) above, Holdings has
contributed to the Company the New Systems.

         Effective immediately following the closing under the Asset
Contribution Agreement, the Company and Holdings have entered into a Second
Amended and Restated Operating Agreement of the Company dated as of January 5,
2001 in order to reflect certain changes and, among other things, to reflect
that Holdings is the new sole member of the Company and that the name of the
Company has been changed.

         Effective immediately following the closing under the Asset
Contribution Agreement, the Manager and the Company desire to amend the Amended
and Restated Management Agreement dated October 1, 1999 by and between the
Manager and the Company (the "Management Agreement"), in order to reflect, among
other things, that (i) the Business now includes the business and operations of
the New Systems and (ii) the name of the Company has been changed.

         NOW, THEREFORE, the Manager and the Company agree as follows:

         1.    Definitions. All capitalized terms used herein and not otherwise
defined herein shall have the same meanings assigned to them in the Management
Agreement. All section references refer to the sections of the Management
Agreement unless otherwise expressly indicated.
<PAGE>

     2.   All references in this First Amendment and the Management Agreement to
the "Midwest Partnership Agreement" shall be deemed references to that certain
Amended and Restated Limited Partnership Agreement of Insight Midwest dated as
of January 5, 2001 by and between Insight and TCI LLC.

     3.   All references in this First Amendment and the Management Agreement to
the "Operating Agreement" shall be deemed references to that certain Second
Amended and Restated Operating Agreement of the Company dated as of January 5,
2001 by and between the Company and Holdings.

     4.   All references in this First Amendment and the Management Agreement to
the "Company" shall be deemed references to Insight Communications Midwest, LLC
(formerly known as Insight Communications of Indiana, LLC), a Delaware limited
liability company.

     5.   All references in this First Amendment and the Management Agreement to
the "Business" shall be deemed references to the business and operations of the
Company, as they may be conducted from time to time, as they are more fully
described in the Operating Agreement, and shall include the business and
operations of the New Systems from and after the date hereof.

     6.   Section 7.3. Section 7.3 is amended in its entirety to read as
follows:

          "7.3   Notices. All notices and other communications given or made
pursuant to this Agreement shall be in writing and shall be deemed to have been
duly given or made as of the date delivered if delivered by hand, by telecopier
device (confirmed by hand delivery or overnight courier service) or by overnight
courier service to the parties at the following address (or at such other
address for a party as shall be specified by like notice):

          if to the Company, to:

          c/o Insight Communications Company, Inc.
          810 7th Avenue
          New York, New York 10019
          Attention: Michael S. Willner
          Telecopier: (917) 286-2301
          Copy to Attention:  Insight Legal Department
          Telecopier: (917) 286-2301

          with a copy to:

          TCI of Indiana Holdings, LLC
          c/o AT&T Broadband, LLC
          188 Inverness Drive West
          Englewood, Colorado 80112
          Attention:  Mr. Alfred Di Blasio
          Telecopier: (303) 858-3456
          Copy to Attention: AT&T Broadband, LLC Legal Department
          Telecopier: (303) 858-5083

                                      -2-
<PAGE>

          if to Manager, to:

          c/o Insight Communications Company, Inc.
          810 7th Avenue
          New York, New York 10019
          Attention:  Michael S. Willner
          Telecopier: (917) 286-2301
          Copy to Attention: Insight Legal Department
          Telecopier: (917) 286-2301"

     7.   Authority. The Manager and the Company acknowledge and agree that they
are entering into this First Amendment pursuant to Section 7.8 of the Management
Agreement.

     8.   Effect of Amendment. Except as amended hereby, the Management
Agreement shall remain unchanged and in full force and effect, and this First
Amendment shall be governed by and subject to the terms of the Management
Agreement, as amended hereby. From and after the date of this First Amendment,
each reference in the Management Agreement to "this Agreement," "hereof,"
"hereunder" or words of like import, and all references to the Management
Agreement in any and all agreements, instruments, documents, notes, certificates
and other writings of every kind and nature (other than in this First Amendment
or as otherwise expressly provided) shall be deemed to mean the Management
Agreement, as amended by this First Amendment.

     9.   General. This First Amendment: (a) shall be binding on the executors,
administrators,estates, heirs, and legal successors of the Manager and the
Company; (b) shall be governed by and construed in accordance with the laws of
the State of Delaware, without regard to conflicts of law principles thereunder;
(c) may be executed in more than one counterpart as of the day and year first
above written.

                           [Signature Page Follows]

                                      -3-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have duly executed this First
Amendment as of the date first above written.

                              INSIGHT COMMUNICATIONS COMPANY, L.P.

                              By: Insight Communications Company, Inc., its
                                  general partner

                              By: ______________________________________________
                                  Name:  Elliot Brecher
                                  Title: Senior Vice President and General
                                         Counsel

                              INSIGHT COMMUNICATIONS MIDWEST, LLC

                              By: Insight Midwest Holdings, LLC, its sole member
                              By: Insight Midwest, L.P., its sole member
                              By: Insight Communications Company, L.P., its
                                  general partner
                              By: Insight Communications Company, Inc., its
                                  general partner

                              By: ______________________________________________
                                  Name:  Elliot Brecher
                                  Title: Senior Vice President and General
                                         Counsel

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