Flooring Tile - Cement Board (CBU) Advice Needed

I hired a contractor to tile my bathroom floor. The tile in my bathroom was installed on a mud/mesh base. The mud/mesh base was only about 5/8" deep, sometimes referred to as a "New Jersey Mud Job". My contractor easily removed the 5/8" mud/mesh base, then installed 1/4 handibacker with thinset and nails onto the subfloor and was about to start laying the tiles. I informed him the the new tiles would be roughly 3/8" lower than the old tiles. This much of a height difference would create several problems with thresholds, cove base tiles, etc etc. My question is, what is the best coarse to take now? Can a second layer of cement board (CBU) be installed over the first? I think this would solve the height difference problem, but would this method cause or create any other problems down the road. I don't want to do anything that will compromise the outcome of the job and I've never heard of putting 2 layers of cement board over a subfloor. Is there a better solution? Any input is appreciated. Thanks mr
__________________

Uhhhh why are you posting again? You received an answer from a couple of Pro's on your other post...the same people would be answering here...

Incase he forgot where it was posted:

http://forum.doityourself.com/flooring-tile/404618-please-need-advice-asap-regarding-tile-contractor.html

That's OK, GG, remember my wife is a nurse, and I am accustomed to the triage (three ways of asking the same question).:o
Either build the floor up with wood, or lay in another layer of CBU. You are worried about the height. As requested in previous posts, give us the desired measurement from the subflooring to the top of the tile that you want.