Posted By jonr on 17 Feb 2016 04:18 PM
There is much less point loading if you glue and nail foam to furring strips.
Even if you will rely on significant external foam for moisture control, try to stick to "breathable in both directions, more so to the cold side".
Use only purpose-made foam board construction adhesive when gluing furring to foam- the solvents of many adhesives would erode or degrade foam insulation.
At R11+ you don't get a heluva lot of "breathing" of water vapor through any foam insulation. The most vapor permeable would be unfaced EPS, which would come in at about 1 perm or a bit less at 3"/R12.6 for 1.5lb density "Type-II" goods. That's right on the Class-II/Class-III vapor retarder boundary. All polyiso products (even fiber faced) would be less than 1-perm, XPS would be about 0.5 perms @ 2.5"/R12.5.
For more money you can use 3"/R12 rigid rock wool which would be over 25 perms, and in your dry climate that still wouldn't present a summertime condensation risk inside the wall cavities during the peak cooling the way it would in the southeastern US. But of course there's no way to make EIFS stick to rock wool. :-)