This work investigates a novel approach in terms of design, configuration, heat integration and optimization of a 6 kWe total energy system fueled with natural gas. Specifically, a Solid Oxide Fuel Cell (SOFC) is used for both electricity generation and fuel reforming, since its exhaust stream fuels a polybenzimidazole (PBI)-based, High Temperature-Proton Exchange Membrane Fuel Cell (HT-PEMFC). The study investigates the possible advantages of such a system in both technical and economic terms. After modeling each component/subsystem, the total system model is optimized with the objective function aiming to maximize the net electrical efficiency of the total hybrid system. The system is optimized with a genetic algorithm-based optimization strategy, reaching a net electrical efficiency of 43.6 %. In comparison to standalone fuel cell systems with the same net electrical power output, the proposed hybrid system outperforms both an HT-PEMFC system and an SOFC system, which perform at net electrical efficiencies of 23.2 % and 40.7 %, respectively. Also, the lifecycle cost for the proposed system is $64,097, which is lower than both standalone HT-PEMFC and SOFC systems. Therefore, with the current high rising costs for natural gas, such highly efficient systems are likely to become important elements of the future energy infrastructure.