How do I combine regular Munchkin with Munchkin Zombies?
Shuffle them all together.

That is why this is a great gateway game but unfortunately it is also a little silly since so many cards have different backings when they are added to the core set. (Sorry, personal opinion)

You are a zombie - that is how you start, you have no powers when there is no mojo - you can discard a mojo to become a plain zombie. 

Shuffle, deal.