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!
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!