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Hybrid energy storage system (HESS) has advantages in coping with the uncertainty of renewable energy and improving the stability of regional integrated energy systems (RIES). Few of the current HESS uncertainty scheduling methods consider both robustness and nonanticipativity, which may result in scheduling strategies that are not feasible in practice. Therefore, this research constructs a HESS (containing electric, thermal, hydrogen and natural gas storage devices) and forms a hybrid energy storage operator (IHESO) with an independent market position based on the HESS to provide energy services. Subsequently, a novel multi-stage distributionally robust optimization (MSDRO) method is established to maximize HESS revenue. Robustness and nonanticipativity can be satisfied in the uncertainty scheduling process of this method. After that, the stochastic dual dynamic integer programming (SDDiP) algorithm is introduced to solve multi-stage nested problems of complex systems. Finally, simulations are conducted in the actual system of three seasons and five scenarios. The conclusions are as follows: 1) The scheduling strategy provided by the MSDRO model and SDDiP algorithm can ensure effective operation based on satisfying robustness and nonanticipativity. 2) Compared with MSO, TSDRO and MSRO, the method proposed can improve the HESS economy and stability, increase renewable energy consumption and reduce carbon emissions. • A multi-stage distributionally robust model was proposed for a multi-energy system. • Robustness and nonanticipativity are satisfied in the scheduling strategy. • HESS combining electricity, thermal, hydrogen and natural gas was proposed. • SDDiP was applied to solve a multi-stage nested model. • This study improves the economy, stability and renewable energy consumption rate. [ABSTRACT FROM AUTHOR]