To reduce patient radiation exposure in mammographic imaging, we investigated the mechanical and radiographic properties of a newly developed carbon-fiber-reinforced foam (CFRF) and its hybrid structures with conventional carbon-fiber-reinforced plastic (CFRP). Flexural stiffness and X-ray transmittance were evaluated for multiple composite designs using three-point bending and transmission measurements under mammographic conditions. The CFRF-only specimen demonstrated a 5% improvement in transmittance and a 25% increase in flexural stiffness compared with CFRP. Moreover, the CFRF thickness can be reduced from 3.4 to 3.2 mm while maintaining equivalent stiffness. Among all designs, the CFRP/CFRF/CFRP sandwich structure achieved the highest transmittance (94.1%) and superior stiffness at the same thickness as conventional CFRP, indicating its high suitability for mammographic platforms. The results suggest that CFRF-based composites offer promising potential to reduce radiation dose while maintaining image quality in breast imaging systems.