It's my understanding that you can't (or shouldn't) do under-floor heating under a floating floor. It's inefficient, for one thing. Also, early under-floor heating was actually too warm and bad for you. People were getting blood clots in their legs and stuff. I can imagine that a cheap mat directly under a floating floor (the sub-floor should be poured over the heating tubes) would have the same issues.
The blood clots thing is something I've heard a lot from my French colleagues. I am guessing this may be one of those things that Europeans believe for whatever reason. I.e., 'air conditioning is bad for your health' and 'fresh corn is only for feeding animals.'