A light weight hybrid heat exchanger core possessing low density and improved thermal conductivity is disclosed. The hybrid core is comprised of a plurality of parting sheets and interposed by a plurality of high thermal conductivity, light weight bridging elements and enclosure bars. These core members are comprised of dissimilar materials. The parting sheets and bridging elements are interconnected by a specially tailored joint which forms form a substantially strong, high thermal conductivity bond. In particular embodiments, carbon-based bridging elements are bonded to metallic parting sheets using a brazed joint. The parting sheets, in certain embodiments, may comprise titanium or Ni-based superalloys or carbon composites, while the carbon-based bridging elements may comprise fiber-reinforced composites. The carbon-based bridging elements reduce the core weight and increase the core thermal conductivity over conventional all-metal designs, while the brazed joint provides for improved leak resistance over all-composite designs.