The increasing proportion of renewable energy introduces both long-term and short-term uncertainty to power systems, which restricts the implementation of energy management systems (EMSs) with high dependency on accurate prediction techniques. A hierarchical online EMS (HEMS) is proposed in this paper to economically operate the Hybrid hydrogen–electricity Storage System (HSS) in a residential microgrid (RMG). The HEMS dispatches an electrolyzer-fuel cell-based hydrogen energy storage (ES) unit for seasonal energy shifting and an on-site battery stack for daily energy allocation against the uncertainty from the renewable energy source (RES) and demand side. The online decision-making of the proposed HEMS is realized through two parallel fuzzy logic (FL)-based controllers which are decoupled by different operating frequencies. An original local energy estimation model (LEEM) is specifically designed for the decision process of FL controllers to comprehensively evaluate the system status and quantify the electricity price expectation for the HEMS. The proposed HEMS is independent of RES prediction or load forecasting, and gives the optimal operation for HSS in separated resolutions: the hydrogen ES unit is dispatched hourly and the battery is operated every minute. The performance of the proposed method is verified by numerical experiments fed by real-world datasets. The superiority of the HEMS in expense-saving manner is validated through comparison with PSO-based day-ahead optimization methods, fuzzy logic EMS, and rule-based online EMS.