We are talking about very different sorts of foam board here.
The stuff you refer to is for making exhibition photo displays and is a rather soft foam between two sheets of glossy cardboard.
PVC foamboard is semi rigid and available in 3mm and upwards sizes. ISTR there are two grades I usually go for the lighter weight one.
I wouldn't describe it as an engineering plastic like nylon sheet would be but it is a lot more resilient than the feeble card backed stuff.
You may have to be a bit careful in the choice of plastic if there are alcohols about. IPA is fairly benign against most plastics but even a trace of methanol will cause stress corrosion cracking of many plastics.
You can acquire random colour offcuts for model making from your local shop sign maker or on eBay. Full sheets cost a fair bit more ~£30/m^2.