The application of composite structures has rapidly expanded in aerospace, automotive, and construction industries, accelerating the development of advanced sandwich panels with diverse applications. In this study, a lightweight sandwich panel was designed and fabricated, consisting of glass fiber–reinforced composite faces reinforced with 0.3 wt% carbon nanotubes and a hybrid polymeric core based on XPS and PU foams. To enhance load transfer and core shear stability, internal GFRP rods were employed as reinforcements. The fabrication process included CNT dispersion in resin, hand lay-up, and cold pressing. The cores were assembled in different sequences and bonded to the facesheets using PVA adhesive. Three-point bending tests were performed in accordance with ASTM C393, and parameters such as peak load, initial stiffness, failure displacement, total absorbed energy, and specific energy absorption (SEA) were evaluated. Results demonstrated that CNT incorporation significantly improved interfacial adhesion and effective modulus, leading to increased stiffness, peak load, and energy contribution. In CNT-containing configurations, peak load reached 700–1000 N, absorbed energy exceeded 20 J, and failure displacement was approximately 50 mm. Comparison of uniform cores revealed that XPS provided higher stiffness, while PU offered greater ductility and final displacement. In hybrid cores, the XPX arrangement (XPS in outer layers) achieved higher stiffness and SEA, whereas the PXP configuration (PU in outer layers) resulted in greater total energy absorption and failure displacement. Overall, optimizing core architecture combined with CNT-reinforced facesheets can simultaneously enhance flexural strength, energy absorption, and ductility, providing a simple and scalable pathway for producing lightweight panels.