To improve the low-carbon efficiency and economy of the integrated energy system, while fully utilizing demand-side flexibility, a hydrogen-containing integrated energy system (HIES) based on green certificate-carbon trading and flexible output of heat and power is proposed. Firstly, the traditional combined heat and power (CHP) is coupled with organic Rankine cycle (ORC) and electric boiler (EB) to allow flexible operation, enabling the power generated by gas turbine (GT) to be supplied simultaneously to the power grid and EB. The heat energy released is simultaneously used for ORC and EB, alleviating the constraints of thermoelectric coupling. Secondly, a green certificate-carbon trading model is constructed by integrating green certificate trading with tiered carbon emission trading, which reduces the system's carbon emissions and improves the consumption of renewable energy. The influence of the green certificate unit price and the renewable energy quota coefficient on the system's optimal scheduling is analyzed. Additionally, the model includes electrolyzers and hydrogen fuel cells, fully considering the diversified utilization of hydrogen energy, thereby improving the system's low-carbon efficiency. Lastly, a day-ahead optimal scheduling model is constructed with the goal of minimizing the total cost of the system. The results demonstrate that this strategy can enhance renewable energy consumption while reducing carbon emissions and total system costs.