You can become both a vampire and werewolf, however you cannot drink anyones blood, leading to your character being stuck at level four vampirism. If you don't mind everyone trying to kill you then you should do the following:
Do the companions quest until you have to drink the blood to become a werewolf, then leave the Underforge and get infected with vampirism, return to the underforge and wait three days
If it works the same way as it did for me, after waiting three days you won't instantly change into a vampire, you have about 5-8 seconds, I waited about 3-4 seconds into this, then drank the werewolf blood. As the game loads up the werewolf part you should get a message telling you that you have turned into a vampire, right after which it will load up with you being a werewolf.