out of wedlock

out of wedlock and outside marriage (of unwed parents; of biological parents not married to each other) — вне брака
born out of wedlock/outside marriage (born illegitimately) — рожденный вне брака; внебрачный (ребенок)
Also born on the wrong side of the blanket

She was born out of wedlock (=was born illegitimately).
We’re living in a country where 53 percent of children born to women under 30 are born out of wedlock, according to government data.
(nytimes.com)

see also
[with child]
[in the family way]
[bun in the oven]
гражданский брак
сожитель