Making boogieman's point a little earlier, it's already happened. Lucio Fulci's 1979 "spaghetti-zombie" movie Zombie, aka Zombi 2.
Ok, then how about this one?
A zombie and a vampire get into a fight, and the zombie bites the vampire, but the vampire also bites the zombie.
Do we get a vampiric zombie, a zombified vampire, both, or neither?