The couple already has a 7-year-old son, Stellan. Bettany, 39, is stepdad to Connelly's 13-year-old son Kai from her previous relationship with photographer David Dugan.
“Becoming a mother has made all the difference in terms of learning to take more responsibility for myself and my life. Parenthood changed the way I do everything. The biggest thing for me is wanting my kids to grow up safely and have happy lives. To me, that''s enough," Connelly told Daily Mirror last year.
The couple, which met each other while filming the Oscar winner 'A Beautiful Mind" tied the knot in Scotland in 2003.