The integration with electrochemical battery (high current and high power for fast power response) and H-2 (high energy density) in district buildings can mitigate grid power fluctuation, and provide energy flexibility for renewable supply and demand-side management, whereas the current literature provides few progresses on synergistic operation to stabilize clean power supply and sustainable transition. In this study, an integrated multi-energy system is formulated, consisting of district buildings, distributed renewable systems, a complementary battery-hydrogen storage, H-2 vehicles, and external energy infrastructures (such as power grid and H-2 station). Multiple energy interactions (e.g., renewable-to-vehicle, vehicle-to-building (V2B), grid-to-building (G2B) and etc.) are deployed to enhance renewable penetration, self-consumption, and mitigate grid dependence. A low-grade heat recovery system is proposed to improve the overall energy efficiency throughout the power-gas-power conversion process. Furthermore, a stack voltage model is applied to quantify real-time fuel cell (FC) degradation magnitudes for hydrogen vehicle (HV) transportation and V2B, which will then be equivalent to operational costs for economic feasibility analysis. After that, considering the four-stage prices of utility grid in Guangzhou, an off-power shifting strategy was proposed and implemented for cost saving, together with comparative analysis on charging/discharging priorities between hydrogen and battery. Results showed that the V2B and the off-peak power shifting strategy can improve the energy flexibility and mitigate the power grid dependence, i.e., the V2B and first charging/discharging priority on H2 systems will improve the off-peak renewable energy shifting from 30% to 35%, and the off-peak grid power shifting from 57% to 75%. Meanwhile, the V2B and the proposed grid power shifting strategy can also save the operating costs for HV owners from 14,375 to 7996 CNY/vehicle center dot a, by 44.4% and the whole energy system from 29.47 to 17.21 CNY/m(2)center dot a by 40.6%. Moreover, the application of off-peak power shifting can slow down the FC degradation by 2.35%, due to the deactivation of V2B process during the off-peak period. However, the low energy efficiency on power-H-2-power conversion will lead to a surge of equivalent CO2 emissions from 10.19 to 19.32 kg/m(2)center dot a by 88.22%. Research results can incentivise the stakeholders' participation in a hydrogen-based renewable-network-loadstorage framework with economic benefits, mitigation on fuel cell degradation, and promote the win-to-win collaborations.