"She had the babies," the star's publicist told People magazine. "They are happy and healthy."
No other details were released about the first children for either actor, People said.
Hunter, 47, is one of seven children, People noted.
The Georgia native met the British actor when they co-starred in the play "By the Bog of Cats" on London's West End.
Notable deaths of 2014 [PHOTOS]
Kris and Bruce Jenner divorcing