The actress and her husband welcome their first child, a son named William


Deadwood actress Molly Parker and her husband, Matt Bissonnette, have welcomed their first child, son William Strummer Bissonnette, PEOPLE has learned exclusively.

William, who was born last Friday in Los Angeles, weighed in at 8 lbs. and 12 oz.

“Both mother and son are doing well,” Parker’s publicist tells PEOPLE.

Parker, 34, plays Deadwood‘s Alma Garret, a New York society woman who reinvents herself in a 19th-century South Dakota town. Recently she co-starred with Ben Affleck and Diane Lane in Hollywoodland.

Up next for the actress: her husband directs her in the upcoming drama, Who Loves the Sun.