Compound helicopters having hybrid propulsion engines

A hybrid propulsion engine for a rotorcraft includes a core turboshaft engine having a gas path and an output shaft that provides torque to a main rotor. A fan module is disposed relative to the core turboshaft engine and is coupled to the output shaft. The fan module has a bypass air path that is independent of the gas path. A thrust nozzle is configured to mix exhaust gases from the core turboshaft engine with bypass air from the fan module and to discharge the mixture to provide propulsive thrust. In a turboshaft configuration, the fan module is closed to prevent the flow of bypass air therethrough such that the thrust nozzle does not provide propulsive thrust. In a turboshaft and turbofan configuration, the fan module is open allowing the flow of bypass air therethrough such that the thrust nozzle provides propulsive thrust, thereby supplying propulsion compounding for the rotorcraft.