A dual valve prosthesis having a self-expanding anchoring frame with first and second prosthetic valve assemblies attached to the anchoring frame is disclosed. Each of the first and second prosthetic valve assemblies includes a balloon-expandable stent structure with a prosthetic valve secured therein. In a disclosed method, the first and second prosthetic valve assemblies include prosthetic mitral and aortic valves, respectively, and the dual heart valve prosthesis is configured to replace both the native mitral and aortic valves of the heart in a single transcatheter heart valve implantation procedure.