The House voted overwhelmingly yesterday to allow all banks, credit unions and savings associations to offer interest on checking accounts.

The bill, approved by a vote of 367-39, now goes to the Senate, which is expected to pass similar legislation.

The legislation is intended to reverse a federal court ruling prohibiting such interest-bearing accounts. That ruling will go into effect Dec. 31 unless Congress passes the legislation and President Carter signs it.

he Court of Appeals for the District of Columbia ruled earlier this year that credit union share drafts and various interest-bearing checking accounts were not authorized by law, even though they were authorized by federal regulations.

But the court agreed to delay its order shutting down such accounts until Dec. 31, to give Congress time to pass a law legalizing the accounts.

The bill had broad support from Congress and credit union members. One supporter, Rep. Gladys Spellman (D-Md.) told the House that the amount of letters and calls she had received from constituents supporting the bill was "unequaled in my experience since I've been here." J. Alvin George, chairman of the board of the Credit Union National Association, said interest-bearing checking accounts are "an extremely important dividend in these days of double-digit inflation."

Rep. Fernard J. St Germain (D-R.I.), chairman of the House Banking sub-committee on financial institutions supervision, said Negotable Orders of Withdrawal -- interest-bearing checking accounts -- had benefitted savings and loan and commercial bank customers in New England.