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, the inflow end having an inflow edge, a plurality of leaflets disposed inside the supporting structure and operative to allow flow in an antegrade direction from the inflow end to the outflow end but to substantially block flow in a retrograde direction from the outflow end to the inflow end, a first material disposed on a luminal surface of the supporting structure adjacent the inflow end, and a second material disposed on an abluminal surface of the supporting structure adjacent the inflow end, the first material and the second material being secured to selected struts of the supporting structure, and separately secured to each other adjacent the inflow edge.