It's very common for children to behave better with dad, because he has the stronger personality, lower voice, etc. It gets their attention and they can't help but respect it.
I suggest you adopt a firmer attitude, voice and look when dealing with your son. None of this "Oh, sweetie, please don't bite mommy. It hurts." No, no. Get right down to his level, look him directly in the eyes, MAKE him look at you and tell him very sternly that he is not to bite you EVER. And then, if you were playing with him, quit and walk away. If you were not, then just walk away. No further attention for a while.
It's kind of like training a puppy not to bite you. When the pup bites, you stop playing and walk away. No further attention. Soon, the pup learns that if/when it bites you, you will not play anymore and they stop the unwanted behavior.