After a delay of more than three months, the Democratic-controlled House yesterday approved and sent to President Reagan legislation authorizing $302.6 billion in military spending for the fiscal year that began Oct. 1.

The measure, adopted with little debate and by a voice vote, allows defense spending this year to increase only with inflation and authorizes funding for hundreds of military programs, including renewed production of lethal chemical weapons.

The Republican-led Senate approved the measure three months ago, shortly after it was approved by a House-Senate conference committee called to resolve differences between House and Senate version of the bill.

But the measure was stalled in the House for months by fierce opposition from Democratic liberals, who felt House conferees had caved in to the Senate in most major areas, from the total price tag to funding for specific weapons systems.

Yesterday, some opponents rose during debate to denounce the legislation, but much of the anticipated anger was missing because of a deal worked out by the House Democratic leadership assuring liberals that their complaints would be dealt with in the defense appropriations measure, which provides the dollars to fund the Pentagon this year.

The bill approved yesterday only authorizes funding levels for defense programs.

The appropriations measure is scheduled for floor action today. Under the agreement worked out by the leadership, it includes several provisions that were dropped by conferees from the authorization approved yesterday.

Among the items approved by the House in June but thrown out by the conference committee were a ban on tests of antisatellite weapons (ASATs), restrictions on release of funds for renewed production of chemical weapons and a freeze on defense spending at last year's level of $292.6 billion. The conference committee instead went with the Senate's $302.6 billion figure.

In addition, the conference committee substantially weakened several House provisions designed to crack down on procurement abuses, limited MX missile deployment to 50 missiles instead of the 40 approved by the House and agreed to give Reagan $2.75 billion for his Strategic Defense Initiative (SDI) instead of the $2.5 billion approved by the House.

"The position of the House was not well represented," said Rep. Barney Frank (D-Mass.), one of those who spoke yesterday against the authorization. "I voted for the House bill this year. I thought it was a pretty good bill. But it came out of the conference committee unrecognizable in area after area."

But supporters of the conference report, including House Armed Services Committee Chairman Les Aspin (D-Wis.), said it was a fair compromise. "We did a good job. We acted in good faith," said the committee's ranking Republican, Rep. William L. Dickinson (R-Ala.).

The appropriations measure up for consideration today limits Pentagon spending this year to $292.6 billion, provides $2.5 billion for SDI, eliminates funding for chemical weapons and restores the ban on testing of ASATs as long as the Soviets observe a similar moratorium.

Several of these provisions are expected to be the focus of extensive debate today.

In other defense matters yesterday, the House Armed Services Committee voted 38 to 2 in favor of a bill that would overhaul the Joint Chiefs of Staff by increasing the power of the chairman.

The bill is designed to to reduce interservice rivalries, but it falls well short of the changes proposed recently by the Senate Armed Services Committee staff, which recommended the elimination of the Joint Chiefs.