How to unlock madhouse difficulty?
Solution 1:
According to this article you must first beat the game on any difficulty:
There are two ways to unlock this mode. The first is to have pre-ordered the game which grants a code that unlocks this mode from the very beginning. The second is to beat the game once on any difficulty mode.
This article (though from the same website) states the same thing.
...or by beating the game once on any difficulty.
I believe the previous entry in the series was also the same, and likely were many of the other Resident Evils.