An H₂ storage system (i.e., an electrolyzer, H₂ tank, and a fuel cell) has received attention for seasonal storage. The H₂ storage system can improve energy conversion efficiency by utilizing recovered heat from the fuel cell in a residential application. This study investigated the potential of a battery-H₂ storage system using the recovered heat to maximize energy self-sufficiency in residential buildings. The entire energy supply network consisted of a photovoltaic, electric heating system, and energy storage systems (i.e., battery, H₂ storage system, and heat tank). To investigate the self-sufficiency performance, four storage cases (i.e., no storage, battery-only, H₂ storage system, and battery-H₂ storage system cases) were introduced to the residential buildings under two electric heating system scenarios (i.e., electric boiler and heat pump system). In addition, these cases were evaluated in terms of economic and environmental performance, and the effects of battery efficiency uncertainty and battery types on energy network performance were analyzed. The findings showed that the battery-H₂ storage system achieved the highest self-sufficiency while reducing the battery capacity because the H₂ storage system compensated for a self-discharge loss of the battery for seasonal storage. Accordingly, the battery-H₂ storage system was the most cost-effective option for minimizing CO₂ emissions in residential buildings. When the battery was used with the H₂ storage system, improving battery energy conversion efficiency was more effective than battery self-discharge rate in reducing CO₂ emissions further. In addition, a lead-acid battery was more cost-effective than a lithium-ion battery but showed low potential to reduce CO₂ emissions and was disadvantageous in terms of physical size.