The prominent problems of renewable energy curtailment and its uncertainty have become a hot topic. To the end, with consideration of environmental friendliness, energy utilization efficiency and operation cost, this paper proposes a hybrid hydrogen–electricity storage system (HHES) operation framework comprising assorted types of coupling devices and carbon capture system (CCS) under ladder-type carbon trading (LCT) mechanism. By considering energy balance constraints, equipments’ operation constraints and erratic rates of RESs and multiple loads, a scheduling model with source-load uncertainties is developed with the goal of minimizing the system’s operation cost and carbon emission. Then, a two-stage tri-level robust model is built to find the optimal scheduling plan under multiple uncertainties given the various sources and loads. The first level is to make an optimal dispatch plan and the second level is to find the worst scenario under the given uncertainty set. The third level aims at enhancing renewable energy accommodation rate and reducing load shedding rate in the worst case. Since the model is formed as a tri-level mixed integer optimization problem, the Column and Constraint Generation (CCG) method is adopted to achieve the optimal result. Finally, numerical analyses are performed. The results show that the proposed approach realizes a flexible dispatch of multiple energy and a high utilization level of multiple storages. Furthermore, this paper studies the influence of uncertainty and uncertainty budget parameters with the comparison of the deterministic model and robust models with different uncertainties. The results show that the proposed HHES has strong robustness and can provide a good reference for energy dispatch.