A prosthetic heart valve includes a frame having a plurality of strut members, an inflow end, and an outflow end. The prosthetic heart valve further includes a leaflet structure situated at least partially within the frame, and a covering disposed around the frame. The covering has a first layer and a second layer, wherein the second layer has a plush surface. The first layer is folded over a circumferential edge portion of the second layer to form a protective portion that extends beyond the strut members in a direction along a longitudinal axis of the prosthetic heart valve.