We are tiling our bathroom and want to tile the built in cupboard, which has 2 doors inset into a wooden frame. So that we don't need to leave a wide gap between the tiles at the edge of the door and the tiles on the frame, we need a hinge that will pull the whole door completely out and clear of the frame, but don't know what will work as there are so many types. We already made a mistake by buying hinges like those on kitchen units which don't work, so don't want to keep buying the wrong ones!
You may be able to find a Euro-style (manufactured by Blum or any other company) hinge... but when you go looking for Euro hinges, BE prepared for a truckload of optional configurations. Some common designs are readily available cheap, off the shelf, while some of the other more exotic designs require buying several pieces after really careful design work.
It'd really help a lot if you could post a sketch of the proposed finished (tiled) doors, showing their inset into the frame and also showing the thickness of the doors & frame, along with some indication roughly how far you'd like each door to open (90 degrees, 180 degrees, 210 degrees, etc).
It sounds like you need a "concealed door hinge" This will let you close the doors flush with the surface and the hinge will not be visible when the doors are closed.
Here is a link to a hinge page with a few possibilities.
We order from McMaster Carr regularly. They are a reputable company.
They also have magnetic push to open latches, so you don't have to have any hardware at all like handles showing either.
Good luck on your project!