I'm not recommending this unless you are just strolling through farm content. As I can see it's limitation.
It just happens that both of us priests don't like playing holy. The other one's mostly shadow but for three healing fights this is how we roll. It's funny as hell on Bladelord though, squeeze in a lot of dps with smite+holy fire and unseen strike barely does any damage with double barrier/spirit shell rotation.
I think ideal setup would be resto druid, holy paladin, and disc priests. I have faith in our fellow tree
We run with one of the following 2 healer setups for our core 10m team:
disc priest / resto dru / resto sham OR disc priest / resto dru x2 and the disc priest goes 'DPS mode' on 2 heal fights, savin our asses when needed with spirit shell blankets etc. Works great for us so far. We sadly would prefer a holy pal, but our main one had to quit wow due to RL GF aggro.
My personal preference would be dpriest/rsham/hpally like so many others have said. This gives you a lot of useful raid CDs with strong mitigation from the priest as well as raw healing power from the shaman and pally.