Methods and apparatus for producing composite-coated rigid flat-rolled sheet metal substrate in which thermoplastic polymeric materials are selected and combined for dual-layer molten-film extrusion presenting a first-contacting tie-layer and an externally-located finish-layer which are simultaneously extruded for a single substrate surface at-a-time; in which tie-layer selection includes an ethylene-glycol modified PET, requiring a substrate-surface temperature between 230.degree. F. and 300.degree. F., and a maleic-anhydride modified polyethylene free of any substrate-surface heating requirement; the tie-layer provides sufficient green-strength-adhesion for a finish-layer selected from PBT, PET, and a combination of PBT and PET; each substrate-surface is separately activated for desired adhesion and separately polymeric coated; dual-surface finishing-processing is carried-out by remelting the coated polymeric materials for completing bonding of the dual polymeric layers on each inorganic-metallic protectively-coated surface of the substrate.