Bear in mind that the hardwood will move at much different rate than the MDF. Laminating the two is considered bad practice in the cabinet making world and I've seen plenty of evidence that would keep me from doing what you suggest without accomodating that differential movement. Mother Nature will win eventually, and she's patient!
It's surprising to many folks how much hardwood moves in response to humidity and temperature swings, some species more than others, but all expand and contract, particularly acoss the grain.
If I were doing it, I mechanically fasten the front without glue, allowing independent movement via slotted or oversize holes.