A prosthetic heart valve (10; 600; 700; 800; 1100) comprising: an annular frame comprising an inflow end and an outflow end and being radially collapsible and expandable between a radially collapsed configuration and a radially expanded configuration, wherein the frame comprises a plurality of struts defining openings; a valvular structure mounted within the frame and comprising a plurality of leaflets that regulate the flow of blood through the frame, wherein each leaflet comprises an inflow surface, an outflow surface, and a cusp edge portion (816; 1116) that is fixed relative to the frame; a sealing member (16; 602; 702; 802) mounted on the frame and comprising an inner layer (34; 604; 704; 804) and an outer layer (36; 606; 706; 806), wherein at least the outer layer (36; 606; 706; 806) is mounted on the outside of the frame, and the inner layer (34; 604; 704; 804) covers at least the openings in the frame between adjacent cusp edge portions of adjacent leaflets and the inner layer (34; 604; 704; 804) does not cover one or more openings in the frame at locations facing the outflow surfaces of the leaflets to permit retrograde blood to flow through the one or more uncovered openings in the frame and into space between the outer layer (36; 606; 706; 806) and the frame; characterized in that (i) the inner layer does not cover any openings in the frame at locations facing the outflow surfaces of the leaflets; (ii) the inner layer is formed with one or more openings along the portions of the inner layer that face the outflow surface of the leaflets to allow retrograde blood to flow through the frame at those locations; or (iii) the inner layer is formed from a porous material that allows blood to flow through the inner layer and the inner layer is formed from a relatively more porous material than the outer layer. an annular frame comprising an inflow end and an outflow end and being radially collapsible and expandable between a radially collapsed configuration and a radially expanded configuration, wherein the frame comprises a plurality of struts defining openings; a valvular structure mounted within the frame and comprising a plurality of leaflets that regulate the flow of blood through the frame, wherein each leaflet comprises an inflow surface, an outflow surface, and a cusp edge portion (816; 1116) that is fixed relative to the frame; a sealing member (16; 602; 702; 802) mounted on the frame and comprising an inner layer (34; 604; 704; 804) and an outer layer (36; 606; 706; 806), wherein at least the outer layer (36; 606; 706; 806) is mounted on the outside of the frame, and the inner layer (34; 604; 704; 804) covers at least the openings in the frame between adjacent cusp edge portions of adjacent leaflets and the inner layer (34; 604; 704; 804) does not cover one or more openings in the frame at locations facing the outflow surfaces of the leaflets to permit retrograde blood to flow through the one or more uncovered openings in the frame and into space between the outer layer (36; 606; 706; 806) and the frame; characterized in that (i) the inner layer does not cover any openings in the frame at locations facing the outflow surfaces of the leaflets; (ii) the inner layer is formed with one or more openings along the portions of the inner layer that face the outflow surface of the leaflets to allow retrograde blood to flow through the frame at those locations; or (iii) the inner layer is formed from a porous material that allows blood to flow through the inner layer and the inner layer is formed from a relatively more porous material than the outer layer. (i) the inner layer does not cover any openings in the frame at locations facing the outflow surfaces of the leaflets; (ii) the inner layer is formed with one or more openings along the portions of the inner layer that face the outflow surface of the leaflets to allow retrograde blood to flow through the frame at those locations; or (iii) the inner layer is formed from a porous material that allows blood to flow through the inner layer and the inner layer is formed from a relatively more porous material than the outer layer.