A stochastic robust optimization model for a hydrogen-integrated energy system (HIES) is proposed in this paper. The model simultaneously considers uncertainties in multi-source-load scenarios, including renewable energy fluctuations, hydrogen demand variations, and electric load randomness. A two-stage robust optimization framework is established to minimize system operating cost under uncertainty while ensuring system reliability and flexibility. A case study based on a regional hydrogen–power coupled network demonstrates that the proposed method effectively balances economy and robustness, achieving superior performance compared with deterministic and conventional robust optimization approaches.