For this to happen, I'd see it as someone who is already a werewolf is then turned into a vampire. They retain their werewolf nature upon rising as a vampire.
Though there is no logic to the supernatural on the show (and it gets retconned whenever desired anyway), I'm still going to use logic and say that the vampire is dead, so diseases that need a living host can't live in it. Therefore, it can't spread its werewolf or vampire nature the way a werewolf can. I'm even going to say no on can a vampire turned by a vampire-werewolf make more vampire-werewolves (though if desired, could seek out werewolves to turn).
I'd say the vampire nature is dominant, perhaps enhanced sense of smell even by vampire standards. They could be killed as normal. If in the form of a wolf...well, that would depend. Nothing really survives beheading. A sword through the heart probably wouldn't kill an undead werewolf, however. Best to stick to crossbows. But how do you know if you're dealing with a vampire with werewolf traits, or an actual werewolf?
I could see an older vampire learning to control the beast within, changing at will.
