We are replacing the shingles on a cathedral roof.
The roof has been insulated from the inside. 8 inches of expanded polystyrene below the roof deck including cut and cobble between the rafters, and 4+ inches of additional eps and mineral wool below that.
The roof is not ventilated.
The shingles will be asphalt.
From what I have read, asphalt shingle roofs are not water or vapor permeable, so using a permeable underlayment will not provide a benefit, because vapor will still not be able to dry through the shingles.