This paper presents a novel co-aperture reflector antenna operating in millimeter-wave (MMW) and infrared (IR) for cloud detection radar. The proposed design combines a back-fed dual-reflector antenna, an IR optical reflection system, and a specialize thin film with IR-reflective/MMW-transmissive properties. Simulations demonstrate a gain exceeding 50 dBi within 94 GHz plush or minus 500 MHz bandwidth, with 0.46{\deg} beamwidth in both azimuth (E-plane) and elevation (H-plane) and sidelobe levels below -25 dB. This co-aperture architecture addresses the limitations of standalone MMW and IR radars, enabling high-resolution cloud microphysical parameter retrieval while minimizing system footprint. The design lays a foundation for airborne/spaceborne multi-mode detection systems.