To effectively address the uncertain risks posed by the inherent intermittency and volatility of wind and solar power output to the Electricity-Heat-Hydrogen Integrated Energy System (EHH-IES) and to reduce carbon emissions, a two-stage distributionally robust optimization scheduling model considering a stepwise carbon trading mechanism is proposed. Firstly, the accurate characterization of the probability distribution of wind and solar power output fuzzy sets is achieved by combining the Wasserstein distance, solving the uncertainty issue of wind and solar power output on the EHH-IES. Secondly, a stepwise carbon trading mechanism is introduced to reduce the carbon emissions of the EHH-IES through policy guidance and economic incentives. Thirdly, for the EHH-IES, a day-ahead and intra-day two-stage distributionally robust optimization scheduling model based on the probability distribution fuzzy set is constructed, and it is transformed into a mixed-integer linear programming model for solving using linear decision rules and strong duality theory. Finally, simulation validation is conducted based on actual wind and solar power data. The results prove that the stepwise carbon trading can significantly reduce the carbon emissions of the EHH-IES, and the proposed model can further ensure robustness under the uncertainty risk of wind and solar power while considering the economy of the EHH-IES.