The House yesterday passed a $9 billion Department of Transportation appropriations bill that includes substantially more money for mass transit programs than the Carter administration sought.

It also forbids the department to require airbags in automobiles.

The bill passed without an amendment that would have hamstrung the Federal Aviation Administration's ability to regulat airspace. The amendment was withdrawn after the FAA backed down from regulatory proposals that had offended the powerful private plane lobby.

A total of $242.5 million in appropriations for various highway and transit programs was added to the bill on the floor yesterday. More than half of the money was specifically for urban transit projects.

The transportation appropriations subcommittee finished marking up the bill in May, and the most visible part of last summer's energy crisis occurred after that.

Long gasoline lines and enormous demand for public transit facilities in big cities on both coasts spurred the additional appropriation, which increased urban transit funding for fiscal 1980 from $1.9 billion to $2.1 billion. The amendment had bipartisan support and slid through on a voice vote with around 30 congressmen on the House floor.

Rep. Robert Duncan (D-Ore.) said substantial improvement in public transit would save energy. But the Department of Energy has claimed that an increase of 15 million transit riders a day would save 350,000 barrels of oil per day, which is less than 1 percent of the oil used by automobiles daily.

The airbag amendment, offered by Rep. John D. Dingell (D-Mich.), forbids the Transportation Department's National Highway Traffic Safety Administration from spending any money on enforcing airbag regulations. However, the amendment permits continued research into the airbag question. It passed, 226 to 185.

Joan Claybrook, administrator of NHTSA and a vigorous airbag backer, said, "I don't think the amendment will have a large amount of substantial effect." NHTSA's regulation mandating airbags does not go into effect until 1982, and the amendment expires Sept. 30, 1980.

A similar amendment passed last year by 95 votes, and Claybrook called the smaller margin of victory this year progress. She called the airbag "the greatest life-saving device ever invented." The Insurance Institute for Highway Safety, in a recent study, concluded that airbags would have saved 39,000 lives between 1975 and 1978 and they been required.

In offering the amendment, Dingell said studies show airbags "are a substantial peril to out-of-position children" and urged more testing.

The FAA, announced 10 days ago that it was withdrawing its controversial proposed rule that would have required all airplanes flying above 10,000 feet to be under air traffic control. Today, that requirement applies only to planes above 18,000 feet.

An amendment threatened by Rep. William H. Harsha (R-Ohio) would have prohibited the FAA from enforcing that rule. Clark Onstad general counsel of the FAA, said in an interview recently that "we did not cave in. We realized we were screwed up."

More than 43,000 protests to the proposed rule were filed with the FAA. The proposal, part of the FAA's plan to reduce likelihood of midair collisions, followed such an accident over San Diego last September that killed 144 people.

As part of the legislative deal, the FAA agreed to drop six airports from 44, around which it was planning intensified airspace control. Each of the 38 airports remaining will receive that control in separate rulemaking actions, if at all, the FAA said.

The bill also contained $40 million extra for Amtrak to fund some passenger lines that Congress ordered in earlier legislation to continue. of the hospital's assets and payment of its creditors.