i think you're being taken for a ride. Only a fool would put multifoil insulation directly under a floor boarding (actually I think only a fool would use multifoil in any application but..)
Multifoils work by having several fleece type layers between impermeable foil layers. Their biggest benefit, when well installed, is in draught reduction - the fleece part/overall thickness is typically incredibly thin and the manufacturer claims that it is as effective as considerably thicker insulation doesn't hold up to scientific scrutiny; the physics of the universe don't change - the basic tenet of insulation is that the greater the thickness of air you can trap in a material that is a poor conductor of heat, the better the insulation factor - air is an incredibly good insulator if you can stop it moving.
If it's free to move the warmed bit floats away to be replaced by a cooler bit, aiding heat loss.
By trapping air (300 mm of fibreglass wool, 150mm of closed cell bubble structure in PIR, even 500mm of hay/shredded paper/flayed denim etc) you create a great insulator. 10mm of multifoil squashed flat by flooring, against a cold concrete slab; useless
If you want to insulate without increasing the height of your floors I'm afraid there isn't a magic bullet; smash the concrete up, remove it, lay a decent thickness (100mm+) of rigid PIR/EPS and pour a new slab (I'd go for a self levelling liquid screed with embedded underfloor heating, every time.
If you can suffer loss of height in rooms, by all means go over the slab with a rigid board, then lay a floating floor eg T&G osb glued together then decorative floor on top of that. Do not use any form of insulation that can be compressed. Compressing robs you of the vital thickness of trapped air; squash all the air out of compressible insulation and it ceases to insulate (screwing it down exacerbates this). Maybe also find a different contractor, as the one you found so far seems a wee bit thick with regard to how insulation works - I wouldn't rate my chances of getting a decent install of anything insulation related by such a person
If you aren't looking to put UFH in, and hence need a nice thick insulation layer to stop your paid for heat soaking into the ground, you can get away with less, but equally you won't notice the same benefit as you would spending the same money on upgrading other insulation on/in the walls and roof as heat loss through a floor accounts for less of the overall house losses than the walls and roof