I’m in the process of redoing the siding and roofing on my 1920s home in climate zone 4 (NJ).  We currently have original tongue and groove sheathing on the entire home with cedar shakes, plaster walls and old blown in insulation which I think has fully settled to the basement at this point.  We have chosen Hardie Plank lap siding for the cladding and I would like to add continuous exterior insulation since insulating from the inside is not an option at this point with the plaster.  I’m trying to get 1/2 inch comfort board but it’s completely out of stock so I’m stuck with choosing a rigid foam board.  

My concern is that my contractor wants to go with no more than 1/2 inch since any more would get really tricky around my windows and doors.  However, 1/2 inch is definitely not enough to prevent condensation on the sheathing during winter months, and with the foam it will act as a vapor barrier not allowing my wall to dry to the outside.  I would like to do a rain screen house wrap between my sheathing and the rigid insulation but I’m nervous that will drastically lower the effectiveness of the insulation.  I’m looking for something vapor permeable that will help insulate the wall assembly, and if it’s not permeable can I still do a rain screen between the insulation and the sheathing?