This study investigates the economic and resilience co-optimization of a decentralized hybrid energy system (HES) within scenarios involving limited energy sources and a hybrid energy storage solution. The HES is comprised of a building-integrated Photovoltaic (PV) system incorporating an adiabatic compressed air energy storage (A-CAES) and batteries, with the main grid, serving as a backup. A two-stage sizing-scheduling model is proposed to optimize the configuration, minimize lifetime costs, and enhance both long and short-term resiliency while achieving an optimal schedule. The charging/discharging transition time of A-CAES is also adopted in the operational model. The results indicate a substantial annual resiliency improvement of approximately 41.1 %, with optimal sizing and energy storage integration. Additionally, they highlight the cost-effectiveness of the PV/A-CAES system while emphasizing the higher self-sufficiency achieved by the PV/A-CAES/battery system, attaining an electrical load management ratio of 47.3 % and a PV self-consumption rate of 96 %, a 6 % improvement over HESs with individual A-CAES. Furthermore, it is presented that under an optimal operational condition, even with the highest PV power availability during grid interruptions, HES relying solely on individual A-CAES could meet 94 % of the load demand. Integrating a fast-response battery enhances this resiliency to 100 %, effectively reducing PV-power curtailment, particularly during grid interruptions and A-CAES transitions.