To balance the competing interests between economy, security, and computational burden caused by the uncertainty of the electricity‑hydrogen integrated energy systems (EH-IESs), a multi-stage coordinated dispatching framework of “day-ahead deterministic dispatching - online security monitoring - intra-day flexible correction” is proposed. The flexibility of the hydrogen energy system is fully exploited and incorporated into the day-ahead dispatching model. To online monitor the future security of the EH-IESs operation in an uncertain environment, a security monitoring method is proposed by combining deep learning and Monte Carlo simulation. The predetermined dispatching scheme may not ensure the security of system operation due to the uncertain output of renewable energy. Thus, an intra-day correction method based on a chance-constrained model and multi-agent deep reinforcement learning is established to determine the correction scheme. Finally, the numerical experiments based on IEEE 57-bus and IEEE 118-bus test systems validate that the proposed method can not only ensure the security of the system but also reduce the economic cost by about 7% and the computational burden by 99%.