Methods and assemblies for attaching leaflets to a frame of a prosthetic heart valve using a connecting skirt are disclosed. As one example, a prosthetic heart valve can include an annular frame comprising a plurality of struts and a valvular structure mounted within the frame and comprising a plurality of leaflets. A cusp edge portion of each leaflet can be connected to the frame by a connecting skirt, where each connecting skirt comprises a central portion and opposing side base portions on opposite sides of the central portion, and each connecting skirt can further comprise side extension portions that extend away from the cusp edge portion of the leaflet and across a portion of cells of the frame that are disposed between cusp edge portions of adjacent leaflets, and covers at least one entire cell of the portion of cells.