Rigid foam on basement ceiling
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If you add batts to your basement ceiling joists, can you then follow on with a layer of rigid? This sounds like it will trap moisture in the joist bay, like if your rim joist leaks, the only place for it to dry to is through the subfloor? If it’s tile above, then it’s vapor closed? Correct?
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Martin wrote an article on this. I read it recently, but don't recall when it was written. IN short, this is not a problem. First, the foam is not a vapor barrier, but a vapor retarder. If you use EPS foam, it is vapor semi-permeable. Second, there shouldn't be any water in between your first floor and your basement ceiling. If your rim joist leaks, it will cause problems regardless of your insulation system. Bulk water leaks must be avoided at all costs. Third, you worry mostly about double vapor barriers if there is any potential for air leakage to bring moisture into contact with a surface cold enough to cause condensation. Even if your basement is pretty cold, there is little likelihood of the upstairs air being humid enough to condense on the topside of the foam insulation.
But why are you insulating the basement ceiling in the first place? Most of the time, it's better to insulate the walls and condition the basement.