A couple suggestions that could work.

Necromancer, has a pet that regains health through attacking, the Necro mainly heals through doing damage to its pet and handing it out.

Dancer, does combos that heal (and do damage) like a melee DPS. small heal into regen into big heal, or small heal into shield into aoe heal, and so on. It then has a number of slots to save these dances into for calling upon aetherial 'backup' dances that repeat the moves. The character physically dancing uses TP, summoning backup dancers uses MP.