Composite leaflets and prosthetic valves incorporating the same are disclosed. An illustrative composite leaflet includes a flexible inner region, which is formed with a synthetic polymeric material, and a flexible peripheral region, which is formed with a remodelable material effective to promote tissue ingrowth. The peripheral region extends from at least a portion of the flexible inner region and is configured to contact a wall of a tubular body passage and thereby promote tissue ingrowth into the peripheral region from the wall of the tubular body passage.
