The median income for American families with at least one wage-earner rose $30 a week from the first quarter of 1979 to the first quarter of this year to $395, but the 8.3 percent gain was outstripped by inflation, the Labor Department reported yesterday.

In the first of a new series of quarterly reports, the department said the median income for families in which both husband and wife work rose 10.5 percent to $529 a week.

Surprisingly, a larger gain in percentage terms -- 11.5 percent -- was reported for families maintained by women. However, the median weekly pay was far lower, rising only from $198 to $220.

The median is the midpoint of a series, such as the array of family incomes.

In this case, exactly one-half of all family incomes are above the median and one-half below it. It isn't the same as an average.

In general, families with two or more wage-earners fared better between the two quarters than did those with only a single worker. Families with no wage or salary workers aren't included.

The median income for married-couple families rose 8.1 percent, from $396 a week to $428. But such families with only one worker experienced only a 6 percent increase, to $306, compared to 9.8 percent for those with two or more workers. The median income for the latter rose from $477 to $524, the department said.

With prices measured by the consumer price index rising more than 13 percent between the two quarters, the real income of virtually every type of family fell behind inflation. The only ones to stay ahead were families maintained by women in which either a family member other than the woman was the only worker or in which there were two or more earners. The latter group had a 16 percent increase as their median income climbed from $317 to $368 a week.

In a separate report, the department said its newly expanded employment cost index showed employe compensation increased 2.7 percent during the three months ended in March.

The new measure includes changes in employer costs for employe benefits as well as wage and salary changes. Comparable data for previous quarters isn't available.

However, the wage and salary portion of the index rose 2.4 percent in the same three months, up from a 2 percent increase in the last three months of 1979. In the 12 months ended in March, wages and salaries climbed 9.1 percent.