Healer DPS rotations tend to be pretty simple, although openers are a bit more complex if you're shooting for fully optimal play. I don't play much SCH, but this is what I use (timer listed is the remaining seconds on the pull timer):

(Start with Selene) > 11s Summon (Eos) > 7s Fey Wind > 5s Infusion of Mind > 3s Cleric Stance > 2s Miasma (Pull happens as Miasma hits) > Bio 2 [Energy Drain + Swiftcast] > Miasma 2 [Shadow Flare + Energy Drain] > Broil 2 [Chain Strategem+ Energy Drain] > Broil 2 [Aetherflow + X] - X being an action up to you. You may use another ED or a healing spell, it's really encounter dependant.

WHM:
5s Infusion of Mind > 3s Cleric Stance > 2s Aero 3 (pull happens as Aero 3 hits) > Aero 2 [Presence of Mind] > Stone 4 > Stone 4 > Stone 4 > Stone 4 [Assize]

AST:
5s Infusion of Mind > 3s Cleric Stance > 2s Malefic 3 (pull happens as Malefic 3 hits) > Combust 2 [Expanded Card] > Malefic 3 > Malefic 3 > Malefic 3 > Malefic 3 [Lord of Crowns] > Malefic 3 [Sleeve Draw] > Malefic 3 [Lord of Crowns if you have it]

This is by no means set in stone, because raid buff timing can change on your opener you want to use as many ogcds/gcds as you can during those windows. For example, I always wait for a full set of buffs (specially Trick Attack) before I use Assize - they share the same cooldown and waiting a few extra GCDs at the beginning to sync it will very rarely, if ever, cause you to miss a use in the fight. It also tends to be beneficial to clip your dots before all the raid buffs go down due to how snapshotting works.

I personally can't say I recommend the full on MH/OH strategy as it ends up gimping one of the healers and can cause you to get bad habits. By default you have two healers with powerful kits at their disposal, and both should be making efficient use of the full extent of their kit to open up DPS opportunities.