The Undead

I won't even get into the root of this question, but what happens if say a zombie bites into vampire brain. Reverse the attack, if you prefer the vampire sinking fang into zombie necks.

Both parties are of the undead, right? In theory, the undead status is communicable - transmitted by zombie saliva to brain contact, vampire - well however you catch vampire cooties.

Would double-undead status cancel itself out then? (Think of the rules of the double negative, here) Would the vampire, after suffering a nasty zombie chomp to the noggin, rejoin the living?

If anybody knows for sure, dial me in. Please.