Michigan code requires R-11 basement walls. My choice is exterior rigid foam or stripping the interior walls. I would prefer exterior foam and use the cement walls as a heat sink. If I foam the exterior what do I cover the exposed foam with that will be above grade? I have heard stucco is a possibility but I have also heard stucco does not fare well with repeated freeze/thaw cycles as we have in Mich. Siding is not an option as code requires 9" of clearance between siding and ground. Question #2 - I am using 5.5" rigid foam insulation in 2x6 walls, should I use thinner foam blocks to leave an air space? And, finally, is 1/2" exterior rigid enough to form a thermal break between wall studs and siding or should it be thicker? Thank you

Randy,
Have you investigated using a PWF (treated wood) basement? PWF is quite popular in Michigan and properly done result in a well insulated dry basement. Using 5.5" of rigid foam between wood suds is a waste because of the thermal conductivity of the studs, any air gap makes it even worse. A much better use of your money is switch the cavity insulation to rock wool bats and boost the exterior foam to 2" or more.

You are zone 5, yes? You'll need R7.5 exterior of stud walls. R7.5 is achieved with 1.5 inches of XPS or 2 inches of EPS. It is hard to answer unless more info is given - where in MI, what foam you're using, etc.

you wrote you're using 5.5" rigid insulation inside a 2x6 stud wall...? Why? If you are putting exterior rigid outside the studs, fiberglass batts are a great option. The better airseal from external rigid and the extra warmth provided keeps the fiberglass performance near 100% so why spend extra money on other more expensive insulation?

There are some sprays to coat the outside of rigid foam. I don't recall the names offhand.

QuiKrete Foam Coating works just fine for finishing & protecting the exposed foam, independent of freeze/thaw issues.  Use only EPS or XPS (and not polyiso) for anything that will be below grade.

Cutting up foam for cavity fill in a 2x6 wall is a waste of foam.  5.5" of R6/inch foam only adds R1.5-R2 to the "whole wall R"  beyond a R20 fiber cavity fill solution, once you factor in the thermal bridging of the framing.  If you also add exterior foam you will have created a moisture trap. Save the foam budget for the continuous exterior sheathing, where it's performance isn't robbed by the thermally bridging framing, fill the cavities with the cheap stuff.

In southern MI (US climate zone5) you'd need at least R7.5 outside the sheathing for dew point control & thermal break, in northern MI (US climate zone 6) it takes R11.25 minimum. 

If you meet or exceed those numbers you don't need any interior side vapor retarder tighter than latex paint, which gives the assembly huge drying capacity and moisture resilience.

You can cheat those numbers if you use a "smart" vapor retarder like Certainteed MemBrain as an air-tight interior side vapor retarder under the wallboard, which will provide good drying capacity while still limiting the moisture uptake during the winter, when the temp at the sheathing may be below the dew point of the interior air.

If using polyiso on the exterior, derate it from it's labeled R to R5/inch for zone 6, R5.5/inch in zone 5, for dew-point control purposes. Alternatively if you split the foam thickness into two layers, with EPS on the exterior and polyiso next to the structural sheathing you can use the labeled value for each.  EPS increases performance at lower temp whereas polyiso loses performance, but with, say 1" of EPS (R4) and 1" of 1lb density foil-faced polyiso (R6) you'll be pretty much at R10 performance across a wide range of temperatures, since the exterior EPS keeps the polyiso in a  warmer higher-performance zone.

IRC 2012 code min for basements is R15 continuous, or R13 in studwalls + R5, not R11.   If the foundation doesn't have a capillary break between the footing and basement wall it's better for moisture control in the basement to split the R between exterior & interior with an inch of foam on the interior.  So, if you put 2" of Type II EPS on the exterior (R8.4) and an inch of EPS (R4) you'll be at R12-ish, meeting MI code, but still R3 shy of IRC 2015.  If you put 1" of a higher-R polyiso on the interior (R6.5)  with 2" of EPS on the exterior you'd be at about R14.9, which is good enough, and it wouldn't isolate the thermal mass of the concrete very much.

Is this new construction or retrofit?

I used the equivalent of "Quikrete Foam Coating" on foam over concrete. Works great in MI. Foam over wood would be a different story (moisture issues).