Bonham Carter gave birth to the couple's second child, whom they have not yet named, in London on Saturday, said Nicki Van Gelder, the actress' agent.
The two met when Burton, 45, directed Bonham Carter, 37, in the remake of the sci-fi movie "Planet of The Apes."
They live in adjoining houses in north London and recently connected the homes with a door.
"I don't know if we'll marry," the magazine Radio Times quoted Bonham Carter as saying. "I find it romantic bearing his illegitimate child and living next door."
Bonham Carter first won fame acting in period films including "A Room With a View" and has starred more recently in "Fight Club" (search) and "Mighty Aphrodite."
Burton has directed movies including "Edward Scissorhands," "Sleepy Hollow" and "Batman."
The couple's first child, Billy Ray, was born on Oct. 6, 2003.