Greyboard is 0.8mm thick recycled pulp board which is cheap and has little or not structural benefit. Mounting board is 1.5mm thick professional framing board and is the best backing for a building to stop it warping over time.
Having built lots of buildings, if you want them to stand up in two years time (humidity in attics etc. love card) the outer sheet is in whatever you want, the inner lining in 1.5mm mounting board and a backing of foamboard behind that. The triple lamination stops it bending, and the mounting board acts as a sponge for any moisture (it's designed for watercolour art)
If none of the above are readily available, the type of card used in pizza delivery boxes, not goodfellas, works great as reinforcing card.
For those in Dublin, Evans Art is the best value card and perspex supplier, I've been a customer since college days in Bolton Street. http://store.evansartsupplies.ie/store/
Richie.