Tile over laminite
You'll have to take the bullnosing off the front of the top, but otherwise I don't see why you couldn't. The bullnosing should be just a plastic type strip in about 3/4" from the front, start at it with a chisel until you get a small area loose. Then (hopefully) it will pull out of it's slot. You may have to put 1/4" concrete board over what's left in order to start with a flat surface.
A second, and possibly better option would be: Remove the laminate CT altogether and build up a new one with 3/4" plywood (not OSB), 1/2" concrete board in a bed of thinset (not mastic...thinset comes dry in a bag and is mixed with water, and is not water soluble) and attached with screws made for concrete board, then tile on top. Finished height would be around 1 1/2" - 1 3/4", but would last a very long time if done correctly.