Love this idea.

If the zombie's body still has some link to the soul such that it could see and react to the ghost, they could make an extremely awkward yet dangerous team.

"Come over this way, buddy! Brains over here!"

"Brainsh?" Shuffle, shuffle.

"Yup, see?" The ghost points triumphantly at a hamster cage. "Lots of juicy little brains to eat!"

"Awww... Tired of mowsh brainsh! WANT HOOMAN BRAINSH!"

Zombie takes another vicious swipe at the ghost but finds only air.

"Why can no eat you brainsh again?"

"As I've explained all evening, I'm ethereal, not really here, sorry, friend. It's mouse or nothing."

The zombie's shoulders slump in disappointment, but he turns to the hamster cage. The hamsters peer back, vaguely uneasy.

"C'mere cute liddle mowshes..."

Clang, squeak, munch, munch, munch.