<PAGE>   1

                                                                    EXHIBIT 3.04

THE MEMBERSHIP INTEREST REPRESENTED BY THIS DOCUMENT HAS NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933 OR THE SECURITIES LAWS OF DELAWARE OR ANY OTHER
JURISDICTION. THE MEMBERSHIP INTEREST MAY NOT BE SOLD, PLEDGED, GIVEN,
HYPOTHECATED OR OTHERWISE TRANSFERRED WITHOUT REGISTRATION UNDER THE SECURITIES
ACT OF 1933 AND APPLICABLE SECURITIES LAWS UNLESS APPROPRIATE EXEMPTIONS FROM
SUCH REGISTRATIONS ARE AVAILABLE AS EVIDENCED EITHER BY THE DELIVERY TO THE
COMPANY OF AN OPINION OF COUNSEL SATISFACTORY TO THE MANAGER OR SUBMISSION TO
THE MANAGER OF OTHER EVIDENCE SATISFACTORY TO THE MANAGER.





                             OPERATING AGREEMENT OF

                          SALEM RADIO OPERATIONS, LLC,

                      A DELAWARE LIMITED LIABILITY COMPANY



<PAGE>   2


            THIS OPERATING AGREEMENT OF SALEM RADIO OPERATIONS, LLC, a Delaware
limited liability company ("Agreement"), is entered into effective as of March
9, 2001, by SALEM MEDIA CORPORATION, a New York corporation (the "Member" and
the "Manager"). SALEM RADIO OPERATIONS, LLC is referred to as the "Company". The
Member hereby agrees as follows:


                                    ARTICLE 1

                            ORGANIZATION AND PURPOSE


            1.1 Formation. The Company has been formed as a limited liability
company pursuant to the Delaware Limited Liability Company Act, 6 Del. C.Section
18-101 et seq. (as from time to time amended including any successor statute of
similar import, the "Act"), subject to the terms contained in this Agreement.
The Company shall be managed by a single Manager. The initial Manager of the
Company shall be SALEM MEDIA CORPORATION, a New York corporation.

            1.2 Name. The name of the Company is "SALEM RADIO OPERATIONS, LLC"
and all business of the Company will be conducted under the name of the Company.

            1.3 Purpose. The business of the Company is to (a) acquire, own,
hold for investment, operate, finance, refinance, manage and/or sell ownership
interests in other business entities and (b) to engage in any other legal
activity which a limited liability company is permitted to do pursuant to the
Act, all as the Manager shall reasonably determine.

            1.4 Registered Office and Registered Agent. The Company's initial
office shall be at 4880 Santa Rosa Road, Suite 300, Camarillo, CA 93012. The
Company's registered agent in Delaware shall be National Registered Agents, Inc.
and its registered office in Delaware shall be 9 East Loockerman Street, City of
Dover, County of Kent, State of Delaware. The registered office and agent of the
Company in Delaware may be changed from time to time by the Manager by filing
the address of the new registered office and/or the name of the new agent with
the Delaware Secretary of State pursuant to the laws of that state.

            1.5 Addresses. The addresses of the Member and the Manager are set
forth on the signature page of this Agreement.

            1.6 Term. The Company's term shall commence upon the filing with the
Delaware Secretary of State of a "Certificate of Formation" and will terminate
on December 31, 2050, subject to earlier termination upon an event of
termination otherwise provided by this Agreement or by law.

            1.7 Documents. The Manager will execute and file the documents
necessary to comply with the requirements of the Act and the other laws of
Delaware for the formation,

                                      -1-
<PAGE>   3

continuation and operation of limited liability companies. The Manager will
further execute and file the documents necessary to qualify the Company to do
business in any other jurisdictions in which the Company shall do business. The
Manager will cause the Company to comply with applicable laws.


                                    ARTICLE 2

                                     CAPITAL


            2.1 Capital Contribution. Concurrently with the execution of this
Agreement, the Member shall contribute cash in the amount of $3,236,000 to the
capital of the Company. The Member shall not be obligated to contribute any
additional capital to the Company.


            2.2 Liability. Except as otherwise provided in this Agreement, the
parties are not obligated to make any advances or contributions of capital to
the Company. Except as otherwise provided in this Agreement or as required by
law, the parties will not be liable for any of the debts of the Company.

            2.3 No Interest on Capital. No interest will be paid to the Member
on its capital contribution.

            2.4 Return of Capital. Except as otherwise provided in this
Agreement, no time has been agreed upon for the contribution of the Member to be
returned to it.

            2.5 Loans from Member. The Member may advance funds to the Company
in its sole, absolute and arbitrary discretion. Any such advances will be
evidenced by the Company's note payable to the Member.


                                    ARTICLE 3

                        PROFITS, LOSSES AND DISTRIBUTIONS


            3.1 Allocation of Profits. All profits of the Company shall be
allocated 100% to the Member.

            3.2 Allocation of Losses. All losses of the Company shall be
allocated 100% to the Member.


                                      -2-
<PAGE>   4

            3.3 Distributions. All cash distributions by the Company shall be
distributed 100% to the Member.

            3.4 Time of Distributions. Distributions shall be made to the Member
as soon as possible after the Manager's determination of the availability of
cash for such purposes, which determination shall be within the reasonable
discretion of the Manager.


                                    ARTICLE 4

                       REIMBURSEMENT OF MANAGER'S EXPENSES

                         AND INDEMNIFICATION OF MANAGER


            The Company will reimburse the Manager for all ordinary and
necessary operating expenses incurred by the Manager in carrying on the
Company's business. The Manager shall not be liable to the Company for any act
or omission suffered or taken by the Manager in good faith, and the Manager
shall be fully protected and indemnified by the Company against all liabilities
and losses suffered by virtue of the Manager's status as the Manager (including
amounts paid in respect of judgments, fines or in settlement of litigation and
expenses reasonably incurred by the Company or the Manager in connection with
any pending or threatened litigation or proceeding) with respect to any action
or omission suffered or taken, including but not limited to any action taken by
the Manager in the formation and operation of the Company or in the financing,
refinancing, improvement, operation and sale of any assets of the Company,
provided that the acts or omissions of the Manager do not constitute gross
negligence, fraud or a criminal act by the Manager.


                                    ARTICLE 5

                        RIGHTS AND OBLIGATIONS OF MANAGER


            5.1 Manager to Manage Business. The business and affairs of the
Company shall be managed by one Manager. The Manager shall be SALEM MEDIA
CORPORATION, a New York corporation, who shall serve as the sole Manager. The
Manager shall direct, manage and control the business of the Company to the best
of its ability and shall devote such time and attention to the conduct of the
business of the Company as is necessary to carry out the purposes and business
of the Company.

            5.2 Powers of the Manager. Except as otherwise provided in this
Agreement, the Manager shall have full and complete authority, power and
discretion to manage and control the business, affairs and properties of the
Company, to make all decisions regarding those matters and to perform any and
all other acts or activities customary or incident to the management of the

                                      -3-
<PAGE>   5

Company's business, including, but not limited to the power:

                5.2.1 To encumber all or less than all Company assets or rights;

                5.2.2 To make all decisions concerning the operational aspects
of the Company;

                5.2.3 To execute and deliver all leases, contracts, deeds and
other instrumentation and documentation in connection with the operations or
business of the Company;

                5.2.4 To borrow money on behalf of the Company and to execute
and deliver in the name of the Company notes evidencing such borrowings and
mortgages, deeds of trust and any other security instruments securing such
borrowings;

                5.2.5 To pay from Company assets all expenses of organizing and
conducting the business of the Company, including without limitation, legal and
accounting fees and costs;

                5.2.6 To execute any and all other instruments and take any and
all other action necessary or desirable to carry out the purposes and business
of the Company;

                5.2.7 To sell, transfer, convey and/or exchange all or any
portion of the property or assets of the Company; and

                5.2.8 To do any other lawful act or thing in furtherance of the
Company's business.

            5.3 Right to Rely on the Manager. The Manager shall have the
absolute authority to bind the Company by its signature alone and anyone dealing
with the Company shall have the right to rely on such authority. Except as
otherwise expressly authorized by this Agreement or by the Manager, no Member
(other than a Member then acting as the Manager), attorney-in-fact, employee or
other agent of the Company shall have any power or authority to bind the Company
in any way, to pledge its credit or to render it liable pecuniarily for any
purpose. Any person dealing with the Company may rely (without duty of further
inquiry) upon a certificate signed by the Manager as to: the identity of the
Manager or any Member; the existence or nonexistence of any fact or facts which
constitute a condition precedent to acts by the Manager or which are in any
other manner germane to the affairs of the Company; the persons and/or entities
who are authorized to execute and deliver any instrument or document of the
Company; or any act or failure to act by the Company or any other matter
whatsoever involving the Company or the Member.

            5.4 Affiliates. The Manager may, in the Manager's absolute
discretion, employ an Affiliate in any capacity on a basis comparable to that
which could be arranged with unaffiliated third parties for comparable service.
Any Affiliate employed by the Company shall have the absolute right (but not the
obligation) to contract with independent third parties in connection with

                                      -4-
<PAGE>   6

the performance of the foregoing service. For purposes of this Agreement, an
"Affiliate" shall include any and all firms and entities, including, without
limitation, corporations, partnerships, joint ventures, trusts, limited
liability companies and associations, which are directly or indirectly owned or
controlled, in whole or in part, by any Member or Manager and/or any of such
entities or any combination of any such persons or entities.

            5.5 Officers. The Manager may appoint and/or remove officers of the
company from time to time in its sole and absolute discretion. Each officer
shall have the title and authority designated by the Manager.


                                    ARTICLE 6

                           DISSOLUTION AND LIQUIDATION


            6.1 Events of Termination: The Company shall, unless otherwise
provided, terminate and dissolve on the happening of any of the following
events:

                6.1.1 Expiration. When the period fixed for the duration of the
Company shall expire pursuant to Paragraph 1.6 (entitled "Term");

                6.1.2 Statutory Dissolution. The happening of any event as
required by Section 18-801 of the Act, unless the business of the Company is
continued by the consent of any remaining Member within 90 days after the
happening of that event and the business of the Company is continued; or

                6.1.3 Disposition of Assets. The sale of all or substantially
all of the Company's assets.

            6.2 Winding Up Affairs and Liquidations. Upon the termination and
dissolution of the Company, the Manager or the persons required or permitted by
law to carry out the winding up of the affairs of the Company ("Liquidator")
will promptly notify the Member of such dissolution; shall proceed to the
liquidation of the assets of the Company by converting such assets to cash
insofar as deemed practicable by the Manager or the Liquidator; will wind up the
affairs of the Company; and, after paying or providing for the payment of all
liabilities and obligations of the Company, will distribute the proceeds of
liquidation and other assets of the Company as provided by law and the terms of
this Agreement. Upon the dissolution of the Company as the result of the
occurrence of an event described in Paragraph 6.1 (entitled "Events of
Termination"), the Manager or Liquidator shall cause to be filed in the office
of, and on a form prescribed by, the Delaware Secretary of State, a Certificate
of Dissolution. Upon the completion of the winding up of the affairs of the
Company, the Manager or Liquidator shall cause to be filed in the office of, and
on a from prescribed by, the Delaware Secretary of State, a Certificate of
Cancellation of Certificate of Formation.

                                      -5-
<PAGE>   7

            6.3 Continuation of Business for Purpose of Winding Up Affairs. Upon
the filing with the Delaware Secretary of State of a Certificate of Dissolution,
the Company shall cease to carry on its business, except insofar as may be
necessary for the winding up of its business..

            6.4 Distributions on Dissolution. The proceeds of liquidation and
other assets of the Company shall be applied and distributed in the following
order of priority:

                6.4.1 Debts. To the payment of debts and liabilities of the
Company (other than (a) any loans and advances that may have been made by the
Member, or amounts owing to the Member, and (b) secured obligations that will be
assumed or otherwise transferred to third parties on the liquidation of the
Company) and the expenses of liquidation;

                6.4.2 Reserves. To the setting up of any reserves that the
Manager or Liquidator may deem reasonably necessary for any contingent or
unforeseen liabilities or obligations of the Company, which reserves shall be
paid over to an escrow holder designated by the Manager or Liquidator to be held
for the purpose of disbursing such reserves in payment of any of the
aforementioned contingencies, and, at the expiration of such period, as the
Manager or the Liquidator shall deem advisable, to distribute the balance
thereafter remaining in the manner hereinafter provided;

                6.4.3 Member Loans. To the payment of any loans or advances that
may have been made by the Member; and

                6.4.4 Members. Any balance then remaining will be distributed
100% to the Member.

            6.5 Assets Other Than Cash. Assets of the Company may be distributed
in kind on the basis of the then fair market value of such assets as determined
by the Manager.

                                    ARTICLE 7

                                 FISCAL MATTERS


            7.1 Books and Journals. The Company will maintain full and accurate
books of the Company at the offices of the Company, showing all receipts and
expenditures, assets and liabilities, profits and losses, and all other records
necessary for recording the Company's business and affairs or required by the
Act. Each Member and such Member's duly authorized representatives shall, during
normal business hours, have access to and may inspect and copy any of such books
and records. Furthermore, upon the request of any Member, copies of any portion
of such books and records shall be delivered to such Member at such Member's
sole cost and expense.

                                      -6-
<PAGE>   8

            7.2 Accountants. The accountants shall be such firm of certified
public accountants as may be selected by the Manager.

            7.3 Bank Accounts. All funds of the Company will be deposited in its
name and in such bank accounts as the Manager shall reasonably determine.

            7.4 Accounting Decisions. All decisions as to accounting matters,
except as specifically provided to the contrary in this Agreement, will be made
by the Company's accountants subject to the approval of the Manager.

                                    ARTICLE 8

                            MISCELLANEOUS PROVISIONS


            8.1 Notices. Any notice required under this Agreement shall be given
in writing (at the address set forth on the signature page for any Member and at
the Company's registered office for the Company) by any of the following means:
(a) personal service; (b) electronic communicating by telegram, telecopying or
fax transmission; (c) overnight courier; or (d) registered or certified, first
class mail, return receipt requested. Such addresses may be changed by notice
given in the same manner as above provided. Any notice sent pursuant to either
(a) or (b), above, shall be deemed received upon such personal service or upon
confirmation of receipt by electronic means (unless confirmation occurs after
4:00 P.M. on the day sent or the day sent is not a business day, in either of
which events confirmation shall be deemed to occur on the next following
business day). Any notice sent pursuant to (c), above, shall be deemed received
on the next business day following deposit with the overnight courier, and any
notice sent pursuant to (d), above, shall be deemed received two (2) business
days following deposit in the mail.

            8.2 Applicable Law. This Agreement shall be governed by, construed
and enforced in accordance with the internal laws of the State of Delaware.

            8.3 Severability. In case any one or more of the provisions
contained in this Agreement or any application of the provisions shall be
invalid, illegal or unenforceable in any respect, the validity, legality and
enforceability of the remaining provisions or the remaining applications will
not in any way be affected or impaired.

            8.4 Captions. The captions and headings in this Agreement are for
convenience only and will not be considered in interpreting any provision of
this Agreement.

            8.5 Gender and Number. Whenever required by the context, the
singular will be deemed to include the plural, and the plural will be deemed to
include the singular, and the masculine, feminine and neuter genders will each
be deemed to include the other.

                                      -7-
<PAGE>   9

            8.6 Execution in Counterparts. This Agreement may be executed in two
or more counterparts, each of which shall be an original, but all of which shall
constitute one and the same instrument.


                                      -8-
<PAGE>   10

            IN WITNESS WHEREOF, the parties have executed this Agreement as of
the date first written above.

ADDRESS                                     MANAGER AND MEMBER


4880 Santa Rosa Road                        SALEM MEDIA CORPORATION,
Suite 300                                   a New York corporation
Camarillo, CA 93012

                                            By: /s/ Jonathan L. Block
                                               ----------------------
                                               Jonathan L. Block, Vice President




                                      -9-