The power switching module includes first and second subassemblies that are superimposed on top of each other to form a stack and that comprise first and second electronic power switches forming a bridging arm, respectively. The module comprises a metal central sheet (LW7) and first and second metal end sheets (LW2, LW12) forming top and bottom ends of the stack. According to the invention, the module also comprises first, second and third metal terminal rods (1, 2, 3) that extend through the stack and open onto at least one of the top and bottom ends thereof, the first, second and third rods being in electrical continuity with the first and second metal end sheets and the metal central sheet, respectively.