The True Blood co-stars are expecting their first baby in the autumn.
Anna, who plays psychic waitress Sookie Stackhouse in the bloodsucker series, fell for Stephen – aka vampire Bill – while filming the pilot in 2007.
They took pains to keep their romance under wraps, and were so successful that much of the cast and crew were unaware.
Carrie Preston, who plays waitress Arlene Fowler in the series, says of their relationship: "I didn't know about it until way into the season. They were very cool and professional about it."
The pair got engaged in 2009 and married a year later in a romantic Malibu ceremony.
Stephen has two children, Lilac, ten, and 12-year-old Billy from a previous relationship.
He recently expressed his desire to extend his family with Anna, who won an Oscar for her performance in the Piano, aged 11.
"We're very busy at the moment but it will happen at some point," he said.