An aircraft power plant has: an electric motor; a compressor; a combustion engine; an output shaft drivingly engageable to a thrust generator for propelling an aircraft equipped with the aircraft power plant; and a transmission including a gearbox having a first input drivingly engaged by the electric motor, a first output drivingly engaging the compressor, a second input drivingly engageable by the combustion engine, and a second output drivingly engageable to the output shaft, wherein the transmission has: a propulsion configuration in which the output shaft and the compressor are drivingly engaged to the electric motor and to the combustion engine via the gearbox, and an auxiliary power unit configuration in which the combustion engine and the output shaft are at rest while the electric motor drivingly engages the compressor.