The couple were presented with the honour at the London Film Festival Awards, which took place at Banqueting House in Whitehall last night (October 20).
"It's good because there's no jealousy at home," said Bonham Carter, before joking: "It's very handy and very thoughtful for them to give us both one at the same time."
The Sweeney Todd star was presented with her award by theatre director Sir Trevor Nunn and went on to thank her parents who were both in attendance, reports Sky News.
"I never thought I was particularly good at this," she told the audience. "I've certainly had my bad reviews over the years, but I kept going.
"My dad's motto is KBO which stands for 'Keep buggering on', so I will, dad."
She also explained that she got into acting because she loved "dressing up".
"I just love pretending, to be honest," she said. "I think it's a lot to do with escape and fantasising. It's as pure as that."
Burton received his accolade from actor Sir Christopher Lee, who worked with the director on films including Sleepy Hollow, Charlie and the Chocolate Factory and Alice In Wonderland.
"Burton is one of the greatest directors of any time," said Lee. "One can only imagine what cinema would look like if Tim had not put his indelible thumb print on it.
"I've worked with Tim several times and I think he's a great director and a close friend. I hope this won't be taken as too much of a hint to appear in his next film!"
Burton, who lives with Bonham Carter and their two children, said 90-year-old Lee "was one of the reasons [he] wanted to be in movies".
"I can't quite believe this because I'm not British," Burton said in his speech. "I grew up on British films, Hammer films, James Bond, The Wicker Man.
"Coming from Los Angeles where you feel like you're in a film business, one of the things I love here is you're constantly reminded it's an art form, so that makes it a special honour."
Burton's latest movie, the animated Frankenweenie, is in cinemas now. Watch him talk to Digital Spy at the film's premiere below: