Two controversial Capitol Hill projects, the extension of the west front of the Capitol building and the creation of a parking lot for House employees on the former Providence Hospital site, were approved yesterday by the House Appropriations Committee.

The Capitol extension, which has received national attention since it involves covering over the last remaining visible section of the original 177-year-old building at a cost of $55 million, sailed through committee without debate.

The parking lot, which has stirred neighborhood fears of traffic congestion and pollution, provoked a spirited discussion. An attempt by Rep. Lawrence Coughlin (R-Pa.) to eliminate the $483,000 projects, to be located at 2d and D Streets SE, was defeated by a roll-call vote of 31 to 18.

The committee's approval of the parking lot outraged a spokesperson for the Coalition of Community organizaitons, composed of 13 Capiotl Hill groups, that is monitoring plans by Congress for expanding its facilities.

"I came home so discouraged today," the spokesperson, Phoebe Bannister, said. "We lobbied (with members of the Appropriations Committee) on Monday. I don't know what our next move will be - to fight it, I guess, on the full House floor, then carry it (the fight) through the Senate."

A Senate source said that body is unlikely to interfere if the full House votes to create the parking lot, which will be located in a residential neighborhood. The two houses of Congress rarely contest each other's proposals.

Both projects were included in a bill providing $929 million to run the House of Representatives and operate several Congress-related functions - including the Library of Congress, the Government printing Office and the General Accounting Office - during the fiscal year that will start Oct. 1. The measure now goes to the House floor.

When the Senate adds its expenses, the bill is expected to total about $1.1 billion.

This year for the first time, the congressional money bill was divided into chapters, with costs of the Congress-related functions separated from those of Congress itself. Rep. George E. Shipley (D-Ill.) chairman of the Legislative Branch Appropriations Subcommittee, said this was done to deflect public and media criticism of "a billion dollar Congress."

Even if it is approved by the full House, as expected, the extension of the west front, faces likely opposition in the Senate. Its principal foe there is Sen. Ernest F. Hollings (D-S.C.).

Under the proposal, the entire facade of the Capitol between the Senate and House wings, would be pushed westward. At its center, the extension would total 22 feet. The project would add about 25 per cent to the existing floor space in the Capitol, providing new cloakrooms, committee facilities and hideaway offices for law-makers.

The broad terraces designed in the 1880s by famed landscape architect Frederick Law Olmsted would remain intact.

The American Institute of Architects, which is spearheading opposition to the project, contends that the project would flatten the facade of the building, lessening the visual distinction between the House and Senate wings.

The parking lot proposal has run into opposition of a different kind. The old Providence Hospital was torn down years ago - so there are no esthetic objections to the 400-space parking lot - but Capitol Hill residents fear additional congestion and pollution.

Congressional supporters of the parking lot contend that staff parking is a major Capitol Hill problem, although Congress has made no efforts to encourage car-pooling for staff members. There is no parking for the public in any government-owned buildings on the Hill and the proposed new lot would be reserved solely for congressional staff.

Backers of the new lot contend that its construction (grading and paving) would improve the appearance of the site, now overgrown with weeds and piled with mounds of dirt.

In other matters involving the congressional money bill, the Appropriations Committee:

Rejected, by a vote of 27 to 13, a move by Rep. Corinne (Lindy) Boggs (D-La.) to provide $225,000 for improvements at the historic Congressional Cemetery on the west bank of the Anacostia River.

Declared, in its official report on the bill, that Congress should "aggressively pursue the development of an adequate mechanism that will insure quality education" for congressional messengers who attend the Capitol Page School.