More than a quarter of the unmarried women who gave birth in a recent year were living with a partner, according to a Census Bureau report that for the first time measured the percentage of unmarried mothers who were not living alone.

“Everybody tends to think of single mothers as being alone with their child, and we wanted to look at whether that was true,” said Jane Dye, the demographer who wrote the report, “Fertility of American Women: 2008.” “We found that 28 percent of these women were living with an unmarried partner, whether opposite sex or same sex.”

While cohabitation has increased enormously over the last generation, the catchall category of “single mother” has often blurred the difference between those living alone and those living with a partner.

But recently, the Census Bureau’s Current Population Survey, one of the sources for the fertility report, added a question on cohabitation to make it possible to measure how many new mothers were actually on their own.