You can change a Conjurer to White Mage and they keep their lvl.
You can change a Gladiator to a Paladin and they keep their lvl.
You can change a Pugilist to a Monk and they keep their lvl.

You change WHM to AST they start don't get to keep the lvl since it's a whole new job.
Atleast that's how I understand it.
I'm not sure if you change back to WMH they keep their previous lvl, never tried it myself.