Can I put polyiso on both sides of a CMU wall?

I have a completely above-grade single-story house with exterior walls made out of 6″ CMU (hollow/unfilled) in Climate Zone 2, no inside framing, you go inside and you see the same CMU blocks that you saw from the outside.
Well, that is until I installed 3/4″ polyiso on the inside a few years ago. Now I’d like to install more insulation, so I planned to install 1.5″ to 2″ of polyiso + furring (rainscreen) + siding on the outside, but now I’m wondering if insulating the exterior and making a CMU sandwich between two impermeable polyiso layers is a mistake since I read somewhere that masonry is supposed to breathe to dry out. I don’t know how the wall is gonna get wet when it’s completely covered, and I don’t know why wet masonry would even be a problem because it can’t rot like wood, but anyway, is this a problem, and if so, what’s the worst that can happen?
GBA Detail Library
A collection of one thousand construction details organized by climate and house part


Replies
Well, I need to move forward on my project, and the materials are already purchased (and half installed before I realized I might be making a mistake), so I'm proceeding with the installation. If a problem develops, I presume the solution will be to remove the polyiso from one side of the wall, so I'd remove it from the inside, because that's only 3/4" of insulation while the outside is 1.5".
But I'm still wondering, what problem might I experience with this kind of vapor sandwich? Rotting my top plates since that's the only direction any moisture can go?
Well, i don't think the concrete is going to care. Plenty of 80 year old block foundations sitting in the mud. I am in zone 5 and have a few spots where the formerly uninsulated poured concrete ended up with foam on both sides. No problem so far...
Masonry doesn't need to breathe, and doesn't need to dry out. Concrete doesn't care if it is wet. the only issue you could potentially have would be moisture wicking up higher in the wall and wetting framing above, but that's probably pretty unlikely in this specific situation that you have. If you're really worried, just get fiber faced roofing polyiso which is a little bit vapor open and will allow some drying and don't worry about it.
Bill
Great, thank you for the replies, guys! And, by sheer coincidence, my polyiso *does* happen to be the fiber-faced roofing stuff. Whew.
I should mention that there's 4-6" of exposed concrete slab below the CMU, so maybe that will promote any drying that needs to happen.