<PAGE>   1
                                                                    EXHIBIT 3.1



                               STATE OF DELAWARE

                        OFFICE OF THE SECRETARY OF STATE                PAGE 1

                         -----------------------------


        I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, 
DO HEREBY CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE RESTATED
CERTIFICATE OF "INTERMEDIA COMMUNICATIONS OF FLORIDA, INC.", FILED IN THIS
OFFICE ON THE SEVENTH DAY OF MAY, A.D. 1992, AT 9 O'CLOCK A.M.














                                     [LOGO]


                                      /s/ Edward J. Freel, Secretary of State
                                      ---------------------------------------
                                          Edward J. Freel, Secretary of State


                                          AUTHENTICATION:      8714777

                                                    DATE:      10-21-97

<PAGE>   2

    STATE OF DELAWARE
    SECRETARY OF STATE
DIVISION OF CORPORATIONS
FILED 09:00 AM 05/07/1992
    921285160 - 214051


                                    RESTATED

                          CERTIFICATE OF INCORPORATION

                                       OF

                  INTERMEDIA COMMUNICATIONS OF FLORIDA, INC.

                             ---------------------

                            UNDER SECTION 245 OF THE

                            GENERAL CORPORATION LAW

                            ----------------------

               The undersigned DOES HEREBY CERTIFY as follows:

                I.     The name of the Corporation is INTERMEDIA
        COMMUNICATIONS OF FLORIDA, INC. (the "Corporation").

                II.    The date of filing of the Corporation's original
        Certificate of Incorporation with the Secretary of State of the
        State of Delaware was November 9, 1987.

                III.    Upon the filing of this Restated Certificate of
        Incorporation, each 2.8 issued and outstanding shares of Common
        Stock, $.01 par value per share, of the Corporation ("Old Common
        Stock"), shall automatically, without any further action by the 
        holder thereof or by the Corporation, be reclassified and deemed
        to be one validly issued, fully paid and nonassessable share of
        Common Stock, $.01 par value per share, of the Corporation ("New
        Common Stock").  No certificates or scrip representing fractional
        shares of New Common Stock shall be issued by reason hereof.  If
        a fractional share would be issuable to any one holder of Old
        Common Stock pursuant hereto, then the number of shares into
        which such old Common Stock will be reclassified pursuant hereto

<PAGE>   3

will be rounded to the next highest number of whole shares of New Common Stock.
Each certificate for 2.8 shares of Old Common Stock prior to the filing of this
Restated Certificate of Incorporation will be deemed upon the filing hereof to
represent a certificate for one share of New Common Stock (subject to the
treatment of fractional interests described above).

       IV.    Concurrently with the filing of this Restated Certificate of
Incorporation, each outstanding share of the Corporation's Series A Preferred
Stock, Series B Preferred Stock and Series C Preferred Stock, $1.00 par value
per share, is being converted (without the payment of accrued but unpaid
dividends thereon), at the election of the Corporation, into fully paid and
nonassessable shares of New Common Stock, all pursuant to the terms and
conditions of such Preferred Stock.

       V.     The Certificate of Incorporation, as heretofore amended, of the
Corporation (the "Certificate of Incorporation") is amended hereby as follows:

       (a)    Article FOURTH is amended to (i) increase the number of shares of
              capital stock which the Corporation shall have authority to issue,
              (ii) eliminate the designations of the Series A, B, C, and D
              Preferred Stock of the Corporation (the "Series Preferred Stock")
              and all powers, preference, privileges, voting, dividend and other
              special or relative rights and qualifications of the Series
              Preferred Stock, including the related prohibition on reissuance
              of such Series

                                      -2-

<PAGE>   4
              Preferred Stock, and (iii) eliminate the parenthetical reference
              in A(2) of Article FOURTH to written actions by stockholders in
              lieu of meetings;

       (b)    Articles FIFTH and SIXTH are hereby deleted in their entirety, in
              part, to eliminate the supermajority voting requirement to effect
              a merger or consolidation;

       (c)    new Articles FIFTH and SIXTH are inserted, among other things, to
              (i) establish the number of directors of the Corporation, with the
              number of directors to be fixed from time to time by resolution of
              the Board of Directors of the Corporation (the "Board"), (ii)
              reorganize the Board into three classes with staggered terms, and
              (iii) eliminate the ability of stockholders to take action by
              written consent; and

       (d)    Article NINTH is amended to conform it to the changes stated
              hereinabove.

              VI.    This Restated Certificate of incorporation was duly adopted
by the Board and authorized by the affirmative vote of the stockholders pursuant
to Sections 222 and 242 of the General Corporation Law of the State of Delaware.

              VII.   The Certificate of Incorporation is hereby amended and
restated in its entirety to read as follows:




                                      -3-

<PAGE>   5

                          CERTIFICATE OF INCORPORATION

                                       OF

                  INTERMEDIATE COMMUNICATIONS OF FLORIDA, INC.


       FIRST:        The name of the Corporation is Intermediate Communications
of Florida, Inc. (the "Corporation").

       SECOND:       The address of the registered office of the Corporation in
the State of Delaware is 15 East North Street, in the City of Dover, County of
Kent.  The name of its registered agent at that address is United Corporate
Services, Inc.

       THIRD:        The purpose of the Corporation is to engage in any lawful
act or activity for which a corporation is to engage in any lawful act or
activity for which a corporation may be organized under the General Corporation
Law of Delaware as set forth in Title 8 of the Delaware Code (the "GCL").

       FOURTH:       The total number of shares of capital stock which the
Corporation shall have authority to issue is 20,500,000 shares, of which
20,000,000 shares shall be classified as Common stock, $.01 par value per share
("Common Stock"), and 500,000 shares shall be classified as Preferred Stock,
$1.00 par value per share ("Preferred Stock").

       The following is a statement of the designations and the powers,
privileges and rights, and the qualifications, limitations or restrictions
thereof in respect of each class of capital stock of the Corporation.



                                      -4-

<PAGE>   6









A.      COMMON STOCK.

             1.   General.  The voting, dividend and liquidation rights of the
holders of the Common Stock are subject to and qualified by the rights of the
holders of the Preferred Stock of any series as may be designated by the Board
of Directors of the Corporation (the "Board") upon any issuance of the
Preferred Stock of any series.

             2.   Voting.   The holders of the Common Stock are entitled to one
vote for each share held at all meetings of stockholders.  There shall be no
cumulative voting.

             3.   Dividends.  Dividends may be declare and paid on the Common
Stock from lawfully available therefor as and when determined by the Board and
subject to any preferential dividend rights of any then outstanding Preferred
Stock.  

             4.   Liquidation.  Upon the dissolution or liquidation of the
Corporation, whether voluntary or involuntary, holders of Common Stock will be
entitled to receive all assets of the Corporation available for distribution to
its stockholders, subject to any preferential or participating rights of any
then outstanding Preferred Stock.

B.      PREFERRED STOCK.

             The Preferred Stock may be issued in one or more series.  The
number, designation and all of the powers, preferences and rights and the
qualifications, limitations or restrictions of the shares of any series of
Preferred Stock may be fixed by the Board as provided in Section 151 of the
GCL.

                                     -5-




   
<PAGE>   7







Different series of Preferred Stock shall not be construed to constitute
different classes of shares for the purposes of voting by classes unless
expressly so provided.

        FIFTH:     The number of directors constituting the entire Board shall
be not less than three nor more than seven as determined from time to time by
resolution of the Board.  The Board shall consist of three classes, designated
as Class I, Class II, and Class III, respectively, with the size of each class
determined from time to time by resolution of the Board.  The Board shall
consist of three classes, designated as Class I, Class II, and Class III,
respectively, with the size of each class determined from time to time by
resolution of the Board; each of which classes shall, however, consist of a
number of directors as equal as possible, with no class having more than one
director more than any other class.  Except for the initial directors in each
class who shall have terms of office of one, two and three years, respectively,
each class of directors shall thereafter have a term of office of three years
and until their respective successors shall have been elected and qualified, or
until a director's earlier resignation or removal.  Any director may resign at
any time upon notice to the Corporation.

        SIXTH:     All action required or permitted to be taken by the
Corporation's stockholders must be effected at a duly called Annual or Special
Meeting (and may not be effected by written consent in lieu thereof).

        SEVENTH:   The Corporation shall to the fullest extent permitted by
Section 145 of the GCL, as amended from time to time, indemnify all persons
whom it may indemnify pursuant


                                     -6-



<PAGE>   8








thereto.  Directors of the Corporation shall have no personal liability for
monetary damages for breach of a fiduciary duty, or failure to exercise any
applicable standard of care, of a director to the fullest extent permitted by
Section 102(b)(7) of the GCL.

        EIGHTH:    Whenever a compromise or arrangement is proposed between
this Corporation and its creditors or any class of them and/or between this
Corporation and its stockholders or any class of them, any court of equitable
jurisdiction within the State of Delaware may, on the application in a summary
way of this Corporation or of any creditor or stockholder thereof or on the
application of any receiver or receivers appointed for this Corporation under
the provisions of section 291 of the GCL or on the application of trustees in
dissolution or of any receiver or receivers appointed for this Corporation
under the provisions of Section 279 of the GCL, order a meeting of the creditors
or class of creditors, and/or of the stockholders or class of stockholders of
this Corporation, as the case may be, to be summoned in such manner as the said
court directs.  If a majority in number representing three-fourths in value of
the creditors or class of creditors, and/or of the stockholders or class of
stockholders of this Corporation, as the case may be, agree to any compromise
or arrangement and to any reorganization of this Corporation as a consequence
of such compromise or arrangement and the said reorganization shall, if
sanctioned by the court to which the said application has been


                                     -7-





<PAGE>   9










made, be binding on all the creditors or class of creditors, and/or on all the
stockholders or class of stockholders, of this Corporation, as the case may be,
and also on this Corporation.  

        NINTH:     The Corporation reserves the right to amend, alter, change
or repeal any provision contained in this Certificate of Incorporation, in the
manner now or hereafter prescribed by law, and all rights and powers conferred
upon stockholders, directors and officers are subject to this reservation.

        IN WITNESS WHEREOF, this Restated Certificate of Incorporation of the
Corporation has been signed, and the statements made herein affirmed as true
under the penalties of perjury, this 27th day of April, 1992.


ATTEST:


/s/ Daniel J. Montague                 /s/ Robert F. Benton
--------------------------             ------------------------
Daniel J. Montague,                    Robert F. Benton,
Secretary                              President



                                     -8-



<PAGE>   10






                              State of Delaware

                   Office of the Secretary of State                    PAGE 1



        I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO
HEREBY CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF
AMENDMENT OF "INTERMEDIA COMMUNICATIONS OF FLORIDA, INC.", FILED IN THIS OFFICE
ON THE TWENTY-FIRST DAY OF JUNE, A.D. 1993, AT 9 O'CLOCK A.M.







                                        /s/ Edward J. Freel
                         [SEAL]         --------------------------------------- 
                                        Edward J. Freel, Secretary of State

                                        AUTHENTICATION:  8714778
                                         
                                                  DATE:  10-21-97




<PAGE>   11
                                                           STATE OF DELAWARE
                                                           SECRETARY OF STATE
                                                        DIVISION OF CORPORATIONS
                                                       FILED 09:00 AM 06/21/1993
                                                          703172017 - 2143051




                           CERTIFICATE OF AMENDMENT
                                      TO
                         CERTIFICATE OF INCORPORATION
                                      OF
                  INTERMEDIA COMMUNICATIONS OF FLORIDA, INC.


                       (Pursuant to Section 242 of the
              General Corporation Law of the State of Delaware)


It is hereby certified that:

             1.  The name of the corporation (the "Corporation") is Intermedia
Communications of Florida, Inc.

             2.  To allow the Corporation's Board of Directors to amend the
Corporation's By-laws without stockholder approval, the Certificate of
Incorporation of the Corporation, as heretofore amended and restated, is hereby
further amended to add the following Article TENTH:

                   "TENTH: The Board of Directors (by action
             taken by a majority of the entire Board of Directors
             then in office) may amend or change the By-Laws of 
             the Corporation in any respect."

             3.  The foregoing amendment to the Certificate was duly adopted by
the Board of Directors and stockholders of the Corporation in accordance with
the provisions of Section 242 of the General corporation Law of the State of
Delaware.

             IN WITNESS WHEREOF, the Corporation has caused this Certificate of
Amendment to be executed on this 4th day of June, 1993.

                                    
                                    INTERMEDIA COMMUNICATIONS OF 
                                    FLORIDA, INC.

 
                                    By: /s/ David Ruberg               6/4/93
                                       ----------------------------------------
                                       David Ruberg, Chief Executive Officer    

Attest:


/s/ Daniel J. Montague
--------------------------------
Daniel J. Montague, Secretary




<PAGE>   12







                              State of Delaware

                   Office of the Secretary of State PAGE 1
                   --------------------------------


        I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO
HEREBY CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF
AMENDMENT OF "INTERMEDIA COMMUNICATIONS OF FLORIDA, INC.", CHANGING ITS NAME
FROM "INTERMEDIA COMMUNICATIONS OF FLORIDA, INC." TO "INTERMEDIA COMMUNICATIONS
INC.", FILED IN THIS OFFICE ON THE THIRTIETH DAY OF MAY, A.D. 1996, AT 9
O'CLOCK A.M.





                                            /s/ Edward J. Freel
                                    [SEAL] ------------------------------------
                                           Edward J. Freel, Secretary of State

                                           AUTHENTICATION:  8714780
                                      
                                                     DATE:   10-21-97





<PAGE>   13
                                                               STATE OF DELAWARE
                                                              SECRETARY OF STATE
                                                        DIVISION OF CORPORATIONS
                                                       FILED 09:00 AM 05/30/1996
                                                             960157445 - 2143051








                           CERTIFICATE OF AMENDMENT

                                    TO THE

                         CERTIFICATE OF INCORPORATION

                                      OF

                  INTERMEDIA COMMUNICATIONS OF FLORIDA, INC.

                  ------------------------------------------
                   Under Section 242 of the Delaware General
                                Corporation Law
                  ------------------------------------------

                  Pursuant to the provisions of Section 242 of the General
Corporation Law of the State of Delaware, the undersigned, being the President
and Secretary of Intermedia Communications of Florida, Inc. do hereby certify
that:

                  FIRST:   The name of the corporation is Intermedia 
Communications of Florida, Inc. (hereinafter referred to as the "Corporation").

                  SECOND:  The Certificate of Incorporation of the Corporation
was filed with the Office of the Secretary of State of the State of Delaware on
November 9, 1987.  The Certificate of Incorporation was Restated and filed with
the Office of the Secretary of State of Delaware on May 7, 1992.

                  THIRD:   The Restated Certificate of Incorporation of the
Corporation is hereby amended to (i) change the name of the Corporation from
Intermedia Communications of Florida, Inc. to Intermedia Communications Inc.,
and (ii) increase the authorized Common Stock from 20,000,000 shares to
50,000,000 shares, so that Article FIRST and paragraph 1 of ARTICLE FOURTH of
the Restated Certificate of Incorporation are hereby amended to read as
follows:

                  "FIRST:  The name of the corporation is Intermedia
Communications Inc. (hereinafter referred to as the "Corporation").

                  "FOURTH:  The total number of shares of capital stock which
the Corporation shall have authority to issue is 50,500,000, of which
50,000,000 shares shall be classified as Common stock, $.01 par value per share
("Common Stock"), and 500,000 shares shall be classified as Preferred Stock,
$1.00 par value per share ("Preferred Stock").

                  "FOURTH:  This Amendment to the Restated Certificate of
Incorporation of the Corporation was duly adopted by the Board of Directors and
by a majority of stockholders of the Corporation




<PAGE>   14








entitled in vote in accordance with the provisions of Section 242 of the
General Corporation Law of the State of Delaware.

        IN WITNESS WHEREOF, the undersigned have executed this Certificate of
Amendment to the Certificate of Incorporation of the Corporation as of this 28
day of May, 1996 and affirm that the statements set forth herein are true and
correct under the penalties of perjury.



                                            /s/ David Ruberg
                                            -----------------------------------
                                            David Ruberg, President and Chief
                                            Executive Officer


                                            /s/ Oscar Williams
                                            -----------------------------------
                                            Oscar Williams, Secretary



                                      2


<PAGE>   15






                              State of Delaware

                   Office of the Secretary of State  PAGE 1
                   --------------------------------




        I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO
HEREBY CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF
AMENDMENT OF "INTERMEDIA COMMUNICATIONS INC.", FILED IN THIS OFFICE ON THE
THIRTIETH DAY OF MAY, A.D. 1997, AT 9 O'CLOCK A.M.







                                            /s/ Edward J. Freel,
                                [SEAL]  ---------------------------------------
                                        Edward J. Freel, Secretary of State

                                        AUTHENTICATION:  8714783

                                                  DATE:  10-21-97





<PAGE>   16
                                                         STATE OF DELAWARE
                                                         SECRETARY OF STATE
                                                      DIVISION OF CORPORATIONS
                                                      FILED 09:00 AM 05/30/1997
                                                         971176982 - 2143051



                            CERTIFICATE OF AMENDMENT
                                        
                                     TO THE
                                        
                          CERTIFICATE OF INCORPORATION
                                        
                                       OF
                                        
                         INTERMEDIA COMMUNICATIONS INC.

                        --------------------------------
                    Pursuant to Section 242 of the Delaware
                            General Corporation Law
                        --------------------------------

          Pursuant to the provisions of Section 242 of the Delaware General
Corporation Law, the undersigned, being a duly authorized officer of Intermedia
Communications Inc., does hereby certify that:

          FIRST:    The name of the corporation is Intermedia Communications
Inc. (hereinafter, the "Corporation").

          SECOND:   The Certificate of Incorporation of the Corporation was
filed with the Office of the Secretary of State of the State of Delaware on
November 9, 1987.  The Certificate of Incorporation was Restated (as amended,
the "Restated Certificate of Incorporation") and filed with the Office of the
Secretary of State of the State of Delaware on May 7, 1992.  A Certificate of
Designation of Voting Power, Designation Preferences and Relative,
Participating, Optional and Other Special Rights and Qualifications,
Limitations and Restrictions of the 13 1/2% Series A and Series B Redeemable
Exchangeable Preferred Stock due 2009 of the Corporation was filed with the
Office of the Secretary of State of the State of Delaware on March 6, 1997 (the
"Certificate of Designation").

          THIRD:    The Restated Certificate of Incorporation is hereby
amended to (i) increase the number of authorized shares of the Corporation's
Preferred Stock, par value $1.00 per share, from 500,000 shares to 2,000,000
shares, (ii) increase the number of authorized shares of the Corporation's 13
1/2% Series B Redeemable Exchangeable Preferred Stock (the "Series B Preferred
Stock") from 60,000 shares to 600,000 shares, and (iii) decrease the
liquidation preference of each authorized share of Series B Preferred Stock
from $10,000 per share to $1,000 per share as follows:

          The first paragraph of ARTICLE FOURTH of the Restated Certificate of
Incorporation is hereby amended to read as follows:

          "FOURTH:  The total number of shares of capital stock which the
     Corporation shall have authority to issue is
<PAGE>   17
     52,000,000 shares, of which $50,000,000 shares shall be classified as 
     Common Stock, $.01 par value per share ("Common Stock"), and 2,000,000 
     shares shall be classified as Preferred Stock, $1.00 par value per share
     ("Preferred Stock")."

          The second paragraph of the first page of the Certificate of
Designation is hereby amended to read as follows:

          "RESOLVED, that pursuant to the authority vested in the Board of
     Directors by the Certificate of Incorporation, the Board of Directors does
     hereby designate, create, authorize and provide for the issue of two series
     of preferred stock having a par value of $1.00 per share, which shall be
     designated as Series A Redeemable Exchangeable Preferred Stock due 2009
     (the "Series A Preferred Stock") and Series B Redeemable Exchangeable 
     Preferred Stock due 2009 (the "Series B Preferred Stock" and, together 
     with the Series A Preferred Stock, the "Exchangeable Preferred Stock"), 
     the Series A Preferred Stock consisting of 60,000 shares, and the Series 
     B Preferred Stock consisting of 600,000 shares provided that no shares of
     Series B Preferred Stock may be issued, except upon the surrender and 
     cancellation of such number of shares of Series A Preferred Stock
     having an aggregate Liquidation Preference equal to the aggregate
     Liquidation Preference of the shares of Series B Preferred Stock so
     issued, and each shall have the following voting powers, preferences and
     relative, participating, optional and other special rights, and
     qualifications, limitations and restrictions thereof as follows:"

          The definition of "Liquidation Preference" in the Certificate of
Designation is hereby amended to read as follows:

          ""Liquidation Preference" means $10,000 per share of Series A
     Preferred Stock and $1,000 per share of Series B Preferred Stock."

          FOURTH:  The additional shares of Preferred Stock created by this
Certificate of Amendment in excess of the 500,000 shares of Preferred Stock
previously authorized may only be issued by the Corporation in connection with
financing transactions, including financing of corporate acquisitions by the
Corporation, and may not be issued for anti-takeover purposes.

          FIFTH:  This amendment to the Restated Certificate of Incorporation
was duly adopted by the Board of Directors of the Corporation and by holders of
a majority of the outstanding shares of capital stock of the Corporation
entitled to vote in accordance with the provisions of Section 242 of the
Delaware General Corporation Law.


                                       2
<PAGE>   18
          IN WITNESS WHEREOF, the undersigned has executed this Certificate of
Amendment to the Restated Certificate of Incorporation as of May 20, 1997, and
affirms that the statements set forth herein are true under the penalties of
perjury.



  
                                           /s/ Robert M. Manning
                                           -------------------------------
                                           Robert M. Manning
                                           Senior Vice President, Chief
                                           Financial Officer & Secretary




                                       3

<PAGE>   19
                              State of Delaware

                       Office of the Secretary of State                 PAGE 1

                       -------------------------------



         I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO
HEREBY CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF
CHANGE OF REGISTERED AGENT OF "INTERMEDIA COMMUNICATIONS INC.", FILED IN THIS
OFFICE ON THE SECOND DAY OF OCTOBER, A.D. 1997, AT 9 O'CLOCK A.M.











                              [SEAL]    /s/  Edward J. Freel
                                        ----------------------------------------
                                        Edward J. Freel, Secretary of State

2143051  8100                                          AUTHENTICATION:   8714785

971355443                                                        DATE:  10-21-97
<PAGE>   20
            CERTIFICATE OF CHANGE OF LOCATION OF REGISTERED OFFICE
                           AND OF REGISTERED AGENT




It is hereby certified that:

          1.   The name of the corporation (hereinafter called the
"corporation") is INTERMEDIA COMMUNICATIONS, INC.

          2.   The registered office of the corporation within the State of
Delaware is hereby changed to 1013 Centre Road, City of Wilmington 19805,
County of New Castle.

          3.   The registered agent of the corporation within the State of
Delaware is hereby changed to Corporation Service Company, the business office
of which is identical with the registered office of the corporation as hereby
changed.

          4.   The corporation has authorized the changes hereinbefore set forth
by resolution of its Board of Directors.


Signed on August 29, 1997.



                                           /s/ Jeanne M. Walters
                                           ------------------------------------
                                            Jeanne M. Walters
                                            Controller/Chief Accounting Officer




                                         DE BCD-:COA CERTIFICATE OF CHANGE 03/96
     STATE OF DELAWARE
     SECRETARY OF STATE
  DIVISION OF CORPORATIONS
  FILED 09:00 AM 10/02/1997
     971332236 - 2143051