A rebellious House and its Democratic-controlled committees battered President Reagan on budget issues yesterday, handing him defeats on housing, college student loans, unemployment compensation and welfare.

In its second such action in two days, the House, on a 343-to-67 roll call, approved a $1 billion emergency measure, this time an appropriation, for a new program to subsidize mortage interest payments of families who buy new homes. The program is meant to help prop up the sagging housing industry, a leading victim of the recession.

The House passed the authorization bill for the program Tuesday. The Republican-controlled Senate is at work on similar legislation, but the Reagan administration opposes it as too costly, and Office of Management and Budget Director David A. Stockman yesterday said he would recommend that the president veto the authorization bill.

Yesterday's $5.9 billion appropriations bill also contains $1.3 billion in supplemental funds for student aid, $321 million more than the president wants, and $1 billion he did not seek for the Government National Mortgage Association, also to help support the housing industry.

The House also, in the same bill, declined to rescind $9.3 billion in previous appropriations for housing assistance to the poor. Reagan had sought rescission.

A House Ways and Means subcommittee, meanwhile, approved legislation that would reverse some welfare cuts Congress made last year and grant up to 13 weeks of additional federal unemployment benefits to workers who exhaust their regular 26 weeks of such federal aid and make a further 13 weeks' federal-state assistance available in some states.

The extra 13 weeks are in response to the rising unemployment rate, now at 9.4 percent, the highest since the Great Depression. Committee aides said the additional benefits would cost $158 million this fiscal year and $627 million in fiscal 1983.

To pay for this the subcommittee proposed dropping the income level at which recipients must start paying income tax on unemployment compensation.

The House Banking Committee Tuesday reported out a $28.7 billion housing bill that virtually ignores the proposals Reagan made in his budget last winter to chop and reshape the main federal housing program for the poor.

These were among the most fundamental cuts he proposed in any welfare program. The housing rescissions the House refused to make yesterday were part of this.

Reagan had requested $2.3 billion for all housing programs, about a 10th of what the committee voted.

It approved $15.6 billion for low-income housing, including funds to keep building new units for low-income families. Reagan had proposed to stop all such new construction.

Earlier, the housing subcommittee had rejected, 23 to 4, his idea of replacing existing subsidies with housing "vouchers" of much less value. It voted to reverse a budget cut of last year, in which Congress agreed that families in federally subsidized housing could be made to pay up to 30 percent of their incomes in rent; it would go back to the old figure of 25 percent. And it voted $1.6 billion in operating subsidies for public housing projects running in the red. Reagan had requested $1.1 billion.

The Senate Banking Committee also has approved more than Reagan sought for the low-income program, but not so much more. The Senate committee did approve partial conversion to a voucher system.

In the debate on the supplemental appropriation bill Rep. Robert S. Walker (R-Pa.), citing the deficit, offered an amendment barring any of the funds in the bill from being used for housing if they would contribute toward a budget that was not balanced.

But his proposal was swamped, 276 to 132, after opponents of his plan pointed out that the amendment would preclude consideration of many of the president's proposals since Reagan did not have a balanced budget either.