You tile contractors will install a wood reducer. Any doors that don't fit can be trimmed.

They'll install a transition strip/reducer that will not be a tripping hazzard. This is extremely common and will not be an issue.

What is under the ceement board? Layer by layer please

@Cabot & Rowe: I wasn't there to see, but I think it goes Tile-cement board-unknown fixing agent or glue that they used- concrete. At least judging from whats under the flooring of the rest of the house, it is possible that the living room might be different.

Is the subfloor wood or concrete? I suspect it's wood and the tile backer was used to solidify the base under the tile.

If its concrete, there is no reason to apply the cement board. All cement board manufacturers require the boards be installed over a layer of thinset (to provide proper support) then be held down with approved fasteners. The latter being very very difficult over a SOG

An update: Talking more with the contractor today, he said that there is in fact more wood under there, above the cement and that he will cut it up and go down to the cement and try to get it to the height so that the tile and the wood are the same height. He said that the tile may still stick up a bit but it will be much less pronounced. I'm not sure if he's going to re-tile or reuse the stuff he already put onto the cement board, I didn't think to ask.

It would help if this time someone was there to take pictures all along the way from demo through finish installation

Wood over cement...interesting... Good thing he has accepted ripping it out and redoing...consider yourself lucky you have a contractor who will work with you to see that you get what you want.

Update 2: Nope, turns out whoever reported cement under there was wrong and it's just wood in that part of the house. They said the tile will have to just stay like that.

They are wrong. The wood flooring can be removed, the subfloor removed, new plywood installed between the joists, CBU installed (or ditra) then tiled.

Honestly if you are tripping on it now, you will be tripping on a transition piece later. On flat surfaces it is best to have them at the same level. The only time an increaser should be used (in my opinion) is a transition from flat to carpet otherwise steps should be made to prepare the floor for a flat continuous surface.

All the materials and work required to give a lower or flat result is a different job altogether. I have seen ceramic done this way many times. Granted, it does not give a flat continuous surface, but it is the more affordable alternative for many homeowners, rather than a complete demolition of the floor surface to build the floor system to the 'correct' height.

If I put something else, other than tile, say pergo, would that need the cement board or could it sit on whatever wood is under there? I know I could just ask the contractor but I feel like I need to be prepared before I talk about anything with him or I get talked over by him, my SO and often my SO's mother.