A prosthetic heart valve includes annularly spaced commissure portions, each of which includes a tip. The stent is formed from a polymeric material, and is specifically configured to perform similarly to conventional metal stents. A first fabric covers each of the tips, and a second fabric covers the first fabric and remaining exposed portions of the stent. A first layer of tissue covers the second fabric, and a second layer of tissue overlies the second fabric. The second layer of tissue includes leaflet portions that extend inwardly between annularly adjacent ones of the commissure portions.