Kevin Mazur/WireImage
The couple, who have been together for about five years, attended Sunday's MTV Movie Awards in Los Angeles, with Fischer showing off her figure in a cream-colored dress – and often rubbing her belly.
Backstage, the couple smooched and greeted a steady stream of friends, one of whom one loudly exclaimed, "congratulations on the baby!" Cohen excitedly answered: "Thank you!"
Both Cohen, 35, and Fisher, 31, began their careers overseas. Cohen, who was born in England and educated at Cambridge, rose to fame in the late 1990s as the wannabe rapper Ali G on British television, and became familiar to U.S. audiences in 2003 when Da Ali G Show began airing on HBO. He became even more popular with the success of last year's comedy, Borat: Cultural Learnings of America for Make Benefit Glorious Nation of Kazakhstan.
Fisher, who was raised in Australia, got her acting career rolling in the mid-'90s on the Aussie soap opera Home and Away, but is best known in the United States as Vince Vaughn's hyperactive love interest in Wedding Crashers.
She told a British newspaper in 2005: "Sacha makes me laugh more than anyone."
Reporting by JULIE JORDAN and JENNIFER GARCIA
