This invention deals with a composite vascular construct, which is formed of a first, blood contacting component and a second, tissue contacting component. Preferably, the present vascular constructs are in the form of a vascular patch or vascular graft with surface-activated, non-absorbable fabric with immobilized biomolecules on the blood contacting surface, and an absorbable, compliant film or microporous sheath on the other surface of the non-absorbable component of the composite graft or patch.