The integrated energy system (IES), known for its flexibility and environmental friendliness, is a promising solution for low-carbon economies and energy efficiency. However, existing IES modeling methods are limited in their ability to explore the synergistic coupling of hydrogen energy across multiple devices, and the scheduling strategies lack market mechanism support. To address this, an optimal scheduling strategy of hydrogen-containing IES is proposed, which comprehensively considers green certificate trading, tiered carbon emission trading, and demand response. Firstly, a hydrogen multi-utilization model based on two-stage power-to-gas is established to promote the use of renewable energy. Secondly, a green certificate-carbon joint trading mechanism is developed to reduce reliance on fossil fuels through market incentives. Finally, an IES optimal scheduling model is constructed with the objective of minimizing economic operating costs, incorporating comprehensive demand response to optimize user-side energy consumption. The model is solved using the CPLEX solver. The results demonstrate that the proposed model effectively achieves multi-energy coupling within IES, enhances the absorption capacity of renewable energy, and reduces carbon emissions.