Burton and Bonham Carter, who have been together since 2001, received the awards at a Saturday ceremony in London on the penultimate night of the film festival, the BBC reported.
"It's good because there's no jealousy at home," Bonham Carter said. "It's very thoughtful for them to give us both one at the same time."
Also honored at the award ceremony was French drama "Rust and Bone," which was named best film.
Sally El Hosaini was named best British newcomer as director and screenwriter for the family drama, "My Brother the Devil." Benh Zeitlin was given the Sutherland Award for the most "original and imaginative feature debut," for "Beasts of the Southern Wild."
The best documentary award went to Alex Gibney for "Mea Maxima Culpa: Silence in the House of God," about sexual abuse within the Catholic church.