since I obviously don't want them doing the same things
As the other poster says, when you think about it you'll find that there are some synergies between almost every type of class. My first group was a Pally, Hunter, two Mages and a Priest, and although there was a certain amount of head-scratching involved every time one of them got a new ability, it worked really well for PvE.

For a Priest and a Mage, there's a surprising amount of commonality and if you play the priest hands-on (with the mage as your drone) then healing will be a doddle.

Off the top of my head (and this is really just thinking out loud):

Priest mind flay (if you go shadow) = mage arcane missiles (i.e. channelled damage).
Priest Smite = Frostbolt / fire spell of choice (spammable direct damage ).
Priest holy nova = arcane explosion (point blank AoE damage).
Priest pet = mage pet.
Priest shield = mage shield (frost barrier / mana shield).
Priest fear perhaps = frost nova (keeps them helplessly in place so you can still nuke them, or at least make good your escape without risking them being feared into running alongside you!)
Priest SW:D = fire blast.
Priest levitate = mage slow fall (handy when you knock people off their flying mounts so you can both land gently alongside their splattered body).

You get the idea.

In practise you'd almost certainly want a one button DPS key that's tied to a castsequence or click macro on each character, bound to the same key.

The only caveat is that it's hard to maximise your DPS for a class that relies on procs (like a Moonkin for example). You'll still pump out damage, but it'll be sub-optimal compared to a "hands-on" player actively responding to procs.