An assembly for the tricuspid orifice of a human heart, comprises an external frame connected to an internal stent carrying a tricuspid valve bioprosthesis and a sealing skirt. The external frame is configured to hold its position in the native tricuspid annulus. The internal stent is connected to the external frame by one or more fixing strands. The sealing skirt covers the interstitial space existing between the external frame and the internal stent. Developments are described which comprise in particular the use of a deformable region of the frame, various alternative embodiments of the sealing skirt, the use of a frame composed of multiple sub-sections, the use of fixing strands between the stent and the frame and of fixing elements for fixing the assembly to the native tissue, the use of sensors and/or actuators, and also the use of a stent in the inferior vena cava. Method aspects are described.