The article discusses a coordinated optimization approach for integrating green hydrogen and turquoise hydrogen in an electric-heat-hydrogen integrated energy system (EHH-IES) to reduce carbon emissions and operating costs. The EHH-IES model considers the willingness of users to purchase zero-carbon energy, the uncertainty of wind power, and the influence of green and turquoise hydrogen coordination. By introducing turquoise hydrogen production technology, the system can effectively reduce carbon emissions. Analysis reveals that considering user preferences for zero-carbon energy reduces operating costs of the system. The distributed robust optimization scheduling model of the EHH-IES addresses the uncertainty in wind power output and further optimizes the system operation. The integration of hydrogen in IES enhances renewable energy utilization rates and overall system efficiency, showcasing the potential of this approach in achieving sustainability goals.