In 2006, she married Jack Black (who cameos in The Muppets), and they have two children; the two met at a private high school. She was the voice of the smitten bunny in Black's film Kung Fu Panda.
Haden is one of the triplet daughters of jazz bassist Charlie Haden, and is the co-creator of the puppet play Imaginary Bear. She has an MFA in experimental animation from California Institute of the Arts. In 2001, she was an assistant animator for the short Lint People.