Which kind of foam do you really have? So far the thread has references to extruded polystyrene (XPS), expanded polystyrene (EPS), and polyisocyanurate. Dow's "blue board" aka Styrofoam and Owens Corning's "pink board" aka Foamular are both XPS. Hot cocoa/coffee cups, made of the tiny white beads/balls, are EPS. IMHO these are the two most common. I don't think I've ever seen either of the polystyrenes faced with anything. Polyisocyanurate is another story; I've seen it faced with foil, thin plastic (like plastic wrap for food), and a fiberglass-reinforced paper. Samples I've seen of polyiso have been white-yellow in color; it looks similar to the polyurethane or latex expanding foams "Great Stuff" etc.
The polystyrenes are dissolved by solvents in many glues and so can be tricky to work with. I recently used 3M Super 77 to bond a piece of XPS to the back side of the drywall cover for an attic access hatch in a building. I left it to cure a day or two before getting back to install the cover and it seemed to have bonded well, but I can't say anything about its long-term hold because I haven't been back to open that attic since. I expect the Super 77 would work on polyiso too.
Polyiso is frequently used in commercial flat roof projects, and it's common to use an adhesive to apply EPDM sheeting to the surface -- the same stuff used for "rubber" roofs on many RVs. You might try a local roofing supply place to see what they offer for polyiso.
Keep in mind that polyiso is hygroscopic: it can absorb and even wick up water. You'll want to install it in such a way that it stays dry. Don't forget about condensation that happens when heating in a cold climate, or when cooling in a warm humid climate.. Building Science Enclosures That Work
is a favorite resource of mine.