Nearly 11 million Americans, including children and other dependents, lack health-insurance coverage because the family breadwinners have lost their jobs, Alice M. Rivlin, director of the Congressional Budget Office, said yesterday.

Because the nation's system of private health insurance is so closely linked to employment, the prolonged recession is having a severe impact on the ability of jobless people to obtain professional health care at a time when they may need it the most, several witnesses told the House Energy and Commerce subcommittee on health and the environment.

This news about another side-effect of hard times comes as Congress prepares to take up the new presidential budget to be submitted on Monday. It also coincides with a rash of studies showing increases in child abuse, infant mortality, alcoholism, heart disease and other sickness and violence aggravated by joblessness.

Hard-hit Michigan recently reported its highest jump in infant mortality since World War II. Yesterday, in a follow-up study, the Food Research and Action Center here reported that a steady, century-long decline in infant mortality rates is being reversed in some cities and states hit by the recession.

The study found such rates rising from 1980 to 1981 statewide in eight states and locally in several major urban centers. The states were Alabama, Alaska, Kansas, Michigan, Missouri, Nevada, Rhode Island and West Virginia.

In Lackawanna, N.Y., the number of infant deaths per 1,000 live births jumped from 16.5 to 26.9; in Johnstown, Pa., from 21.3 to 25.2, and in Wilkes-Barre, Pa., from 11.1 to 18.9. In Baltimore, the overall rate did not increase, but the rate for white infants did.

The nationwide death rate for minority infants continues to be at least double that of whites.

About two-thirds of the nation's infant deaths are associated with low birth weight, the center noted. "More babies are dying because their mother lacked basic food and health care," Director Nancy Amidei said.

Any government-imposed solutions to the health insurance problem, public or private, that might work fast enough to help those already in need, however, were described as costly and politically elusive.

For example, Rivlin said, extending Medicare in fiscal 1983 to cover those who had lost benefits because of unemployment would cost about $6 billion and "would thus add significantly to the federal deficit."

Other options involve long-term programs such as a "piggyback" addition to the existing unemployment compensation program that would provide some health insurance.

"This tragic byproduct of unemployment may, in the not-so-long run, cost the nation as much in damaged and lost lives as the unemployment itself," United Auto Workers President Douglas A. Fraser told the panel. Although he favors national health insurance as the best long-run answer, he proposed a mix of private and public measures as workable.

Meanwhile, Rep. Henry A. Waxman (D-Calif.), who chairs the subcommittee, said he intends to spread the word among the jobless that about 4,000 hospitals nationwide, as recipients of federal funds, are legally obligated to provide at least some care to those unable to pay.

About 5.3 million laid-off workers have lost health insurance coverage they had at work, Rivlin said, and those numbers continue to grow. Although health benefits usually continue briefly after a job loss, almost 70 percent of those laid off have been jobless for five weeks or more and have exhausted that extended coverage.

Even though the number of families with two wage earners has increased, they comprise fewer than half of all working families. By Rivlin's estimates, only about one-fourth of them have separate insurance policies that would maintain a family's coverage if one wage earner loses a job.

In the private work force, which includes nearly three-fourths of all U.S. employment, nearly 90 percent of all employes are in firms that offer health insurance as a fringe benefit. About 20 million more people, in and out of the work force, lack coverage for other reasons, Rivlin noted.