What behavior is this?

Hi, all. I have a Pit Bull mix and a Bichon Frise. My brother found the mix on the side of the road somewhere and my sister had to move and couldn't take the Bichon with her. I love them almost more than anything in the world.
The mix will make biting motions on the Bichon everytime she is near him. She bites very close to the skin without actually biting the skin. It makes me think she might be trying to get fleas off of him. She will also do this to my cat. They both like it.
I've never seen a dog do this and I've had lots of dogs over the years. Does anyone know why she does this? It is like an obsession with her.