A prefabricated cover board has a high-density polymer or predominantly polymer material core layer having a density between 6 lbs/ft.sup.3 and 25 lbs/ft.sup.3. A prefabricated roofing panel composite includes the cover board and an insulation board that has a low-density polymer or predominantly polymer material foam core layer having a density less than 6 lbs/ft.sup.3. The cover board may have a waterproofing membrane forming the top major surface of the cover board. When making the roofing panel composite, the low-density foam core layer of the insulation board may be formed with the high-density core layer of the cover board being currently or subsequently formed over and bonded to a top major surface of the low-density foam core layer in the same operation or preformed insulation boards may be fed into a production line with the high-density core layer of the cover board being formed over and bonded to top major surfaces of the low-density foam core layers of the insulation boards.