A coordinated scheduling model based on two-stage distributionally robust optimization (TSDRO) is proposed for integrated energy systems (IESs) with electricity-hydrogen hybrid energy storage. The scheduling problem of the IES is divided into two stages in the TSDRO-based coordinated scheduling model. The frst stage addresses the day-ahead optimal scheduling problem of the IES under deterministic forecasting information, while the second stage uses a distributionally robust optimization method to determine the intraday rescheduling problem under high-order uncertainties, building upon the results of the frst stage. The scheduling model also considers collaboration among the electricity, thermal, and gas networks, focusing on economic operation and carbon emissions. The fexibility of these networks and the energy gradient utilization of hydrogen units during operation are also incorporated into the model. To improve computational efciency, the nonlinear formulations in the TSDRO-based coordinated scheduling model are properly linearized to obtain a Mixed-Integer Linear Programming model. The Column-Constraint Generation (C&CG) algorithm is then employed to decompose the scheduling model into a master problem and subproblems. Through the iterative solution of the master problem and subproblems, an efcient analysis of the coordinated scheduling model is achieved. Finally, the efectiveness of the proposed TSDRO-based coordinated scheduling model is verifed through case studies. The simulation results demonstrate that the proposed TSDRO-based coordinated scheduling model can efectively accomplish the optimal scheduling task while considering the uncertainty and fexibility of the system. Compared with traditional methods, the proposed TSDRO-based coordinated scheduling model can better balance conservativeness and robustness.