A prosthetic heart valve includes an annularly collapsible and re-expandable supporting structure extending between an inflow end and an outflow end and including a plurality of struts, a plurality of leaflets disposed inside the supporting structure and operative to allow flow in a first direction from the inflow end to the outflow end and to substantially block flow in an opposite direction from the outflow end to the inflow end, a sheet circumferentially disposed on an inner surface of the supporting structure and coupled to the supporting structure, a reinforcing core coupled to at least one of the plurality of leaflets, and a plurality of stitches coupling the reinforcing core to the sheet and one of the plurality of leaflets.