A roof covering material is provided, as well as its method of manufacture, wherein a substrate, preferably of a fibrous material is provided, with a bituminous material, preferably asphalt coating, on opposite surfaces thereof with granules being applied to an upper surface thereof and at least partially embedded in the bituminous material and with a discontinuous top layer applied to the granule/bituminous material. The discontinuous top layer is preferably a polymeric material, and openings are provided therein, for passage of fluids therethrough, to avoid moisture, volatiles, and other fluid materials from being trapped beneath the top layer. Various techniques for application of the various materials, and for chemical treatment, are likewise provided.