Exterior insulation roof deck

We are located in northern NJ. We are starting an energy retrofit. We will have 3” mineral wool on the exterior walls. For the exterior roof deck, should we go with polyiso or mineral wool as well. It is spec’d at 4” polyiso with staggered joints. Moreover, there will not be spray foam on the interior roof deck (only r30 batts). The roof is unvented. Singled asphalt roof will be the roof material. Is it necessary to externally vent the roof?
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My understanding of the question is that they are installing 4" rigid on top of the deck and R30 batts under it. This gives close to a 50-50 ratio of fluffy to fiber and should be safe for this climate zone. In fact, that is nearly an ideal roof design, but a bit expensive. I always suggest polyiso foam for roof applications. You can probably find some used on Craig's List for less than half the price of new foam. The paper or fleece faced foam is appropriate. I would prefer not to use the foil-faced foam though it probably doesn't make much difference in this assembly.
Peter,
Reading IRC R 806.5 I think you are right. I have deleted my post.
Yes, correct, roof sheathing -> underlayment -> foam -> plywood/roof sheathing -> underlayment -> shingles. Then existing pink r30 in the interior bays.
I appreciate the feedback- thank you!