A roofing membrane includes a substrate sheet formed of a thermoplastic vulcanizate (TPV) and a film layer of thermoplastic polyolefin (TPO) adhered to at least one surface of the substrate sheet. The TPV preferably includes a copolymer of ethylene and a carbonyl containing monomer dynamically vulcanized in a polyolefin thermoplastic, preferably metallocene-catalyzed polyethylene. A scrim reinforcement layer is optionally embedded in the TPV layer. When installed on a roof substrate, the membrane can be sealed by heat welding the seams of the membrane sheets.