The House Appropriations Committee reported out an $11.2 billion funding bill yesterday for the Interior Department and related agencies which includes a controversial ban on oil drilling off the northern coast of California. Interior Secretary James G. Watt had sought to push ahead with the drilling despite objections from environmentalists and California congressmen.

In another slap at the administration, the bill, although it comes $7 million under President Reagan's recommendation, includes $150 million for the purchase of federal park and recreation land. Watt had sought a moratorium on new purchases. The committee, however, agreed to cut out the current budget's $235 million state land purchasing program.

The Interior bill and a $63.3 billion Housing and Urban Development funding bill, the first appropriations measures of the year to be reported out of committee, will reach the floor after Congress's July 4 recess. Sen. Paul Laxalt (R-Nev.) predicted that it would take Congress until December to finish appropriating money to run the government, despite the administration's desire to speed up the process.

The Interior bill gives a new lease on life to the District's National Aquarium by transferring it from the Commerce Department to the National Zoo, a division of the Smithsonian. The zoo is expected to try to find new quarters for the aquarium, which the administration had sought to dismantle.

In what may be a controversial move, the bill appropriates $3.4 billion for the Strategic Petroleum Reserve, the government's oil stockpiling program, as an on-budget, rather than off-budget, item. The House Budget Committee voted to keep the petroleum reserve off-budget in order to make room for other spending in its restrictive budget bill.

The Interior bill also includes only slight cuts for the endowments of the arts and humanities which the administration had sought to reduce by 50 percent.

The HUD bill, which also includes funding for the Veterans Administration, and National Aeronautics and Space Administration and other agencies, represents a $6.3 billion cut -- 10 percent less than current funding. It is $190 million over Reagan's request.

Two controversial items the administration sought to abolish also were funded: the Solar Bank at $50 million and the National Consumer Cooperative Bank at $53 million.

The HUD bill cuts funding for the Environmental Protection Agency from the current $4 billion to $1.4 billion, mostly by eliminating the grants programs for building community sewer plants.