As a healer, there are a few ways that I deal with Living Dead.

1.) WHM: Benediction - this is the only way that will instantly clear the debuff.
2.) WHM: Pre-cast Regen (timing based on how quickly the tank's HP is going down - usually estimating ~1GCD before the debuff occurs) > Tetragrammaton > Afflatus Solace > Thin Air > Presence of Mind > Swiftcast (optional) > Cure II until debuff is cleared
3.) AST: Pre-cast Earthly Star (timing for Giant Dominance on detonation) > Lucid Dreaming > Diurnal Aspected Benefic (same as WHM Regen timing) > Essential Dignity > Lightspeed > Essential Dignity > Swiftcast + Benefic II > hard cast Benefic II until debuff is cleared.

SCH I don't really play often, so I don't have a good answer for how SCH can deal with the Walking Dead debuff. Obviously solutions 2 and 3 are... less than ideal, but they do work with a relatively high degree of success.