Holy Priests are the most versatile healers, and can certainly heal a tank. Our single-target capability is still lower than Paladins, but on a par with Druids and Shammies. Provided that you keep renew ticking (Heal Chakra does this) and inspiration up, you can heal a tank.
HOWEVER, your healing combo is Shammy-Disco Priest-Holy Priest. Given that shield-spamming is now a big no-no and Grace has changed, Disco Priests have lost some of their potential as raid healers. With the amount of AoE damage and the power of Holy AoE healing, I think it is illogical to have a holy priest on a tank and a disco priest on the raid.
I have the luxury of both specs, and I switch between them depending on the fight. Holy priests can tank heal, and disco priests can raid heal, but right now I think that you should play to your strengths, which means Holy focussing on the raid primarily.
For the record, I use the following specs as a raid healer:
Omnitron System: Holy, because most of the unavoidable damage is AoE
Magmaw: Holy, because there is high AoE damage and you are grouped up tightly for Serenity
Maloriak: Disco, because there is lots of single-target spikes and PW:B is OP
Chimaeron: Holy, because shields are utterly worthless
Halfus: Holy, because HoTs are win in P2 and flash heal is needed a lot (and disco flash heal is pants)
Valiona: Holy, for AoE dmg plus Body & Soul
Twilight Council: Holy, for body & soul plus big AoE damage plus quick flash heals & empowered renew
Conclave of Wind: Disco, because I'm primarily a tank healer
So, that's 1 fight out of 7 where I think disco is stronger for raid healing. Holy's strongest spells (in terms of HPM) are lightwell, PoM, PoH, renew, CoH & binding heal. Almost all of these are multi-target spells. Make sure you're using binding heal whenever you take damage, or flash heal if you don't, to build up serendipity for quick PoH casts. Holy Word: Serenity isn't that efficient in 10-man, but still very potent, and it ticks away whilst you get on with other things, so is worth casting whenever 5 or more ppl are stacked.
Disco's best spells are Penance, GH, PoM and PW:S, with PoH powerful if the automatic DA is going to be used up. Shield spamming is to be avoided; it's not efficient, it only absorbs 10-12k each, and since Rapture changed it will no longer get you any mana back. Just awful.