"She had the babies," the star's publicist tells PEOPLE. "They are happy and healthy."
No other details were immediately available. These are the first children for The Piano star and the British actor.
Hunter, who is one of seven children herself, voiced the role of the mother Helen Parr (also known as Elastigirl) in 2004's animated movie smash The Incredibles.
Besides winning the Oscar in 1993 for The Piano, she also received Academy Award nominations for her roles in Broadcast News, The Firm and Thirteen.
The Georgia-born actress and MacDonald, who appeared in The Thin Red Line, met in November 2004 while costarring in the London West End production of playwright Marina Carr's By the Bog of Cats, in which she played a woman abandoned by her lover of 14 years, played by MacDonald.
Up next for Hunter: She has signed on to appear with her former Broadcast News costar William Hurt in the film Downloading Nancy.