A transmission assembly for a motor vehicle having a gearbox including a clutch, a clutch-release device, a reversible rotary electric machine provided with a rotor provided with a central opening, and an intermediate shaft between the clutch and the rotor of the electric machine, the shaft supporting the clutch-release device at the front and being inserted in the central opening of the rotor. The transmission assembly includes a dry friction clutch provided with a reaction plate, and comprises, at the front, a damping double flywheel configured such as to be attached to the crankshaft of the heat engine of the vehicle and to form the reaction plate of the dry friction clutch and, at the rear, a torsion damper configured such as to be rotatably connected to the input shaft of the gearbox, the rotor of the electric machine being attached to the torsion damper.