Now, I know what you’re thinking. You’re thinking ‘what?’ I don’t blame you, but this idea popped into my head, and it wouldn’t leave, so now it’s placed into written form, to inflict upon you all.
Could a zombie infect a vampire? Well, vampires are said to be undead, and therefore I presume immune to infection. How can you infect dead tissue? It might not be pleasant for a vampire to be bitten (I mean, biting hurts right?), but I don’t see how a vampire suffers ill effects from a zombie bite.
Would a vampire bite turn a zombie? Well, zombies are often considered to be undead as well, so it raises the question of whether or not a vampire’s supernatural bite would any effect on a dead creature. Probably not.
Ultimately, it seems like vampire versus zombie would be a stalemate in terms of infecting one another, but overall, a vampire (in most lore anyway) retains its mind, so a vampire would know how to defeat a mindless, shambling zombie. In the wake of being unable to turn a zombie, and considering vampires and zombies fight for the same resources (humans!), the vampire would be advised to go on a zombie-destroying spree.