With the continuous advancement of new power systems and energy interconnection, building an efficient, low-carbon, and economical energy supply system is crucial for the development of the dual carbon strategy. To this end, this paper proposes an optimized operation strategy for an integrated energy system (IES) that considers multi-type demand response and diverse utilization of hydrogen under a joint mechanism of green certificate and carbon trading. Firstly, to fully leverage the regulatory capabilities of demand-side resources, a multi-type demand response model is constructed, encompassing price-based, incentive-based, and substitution-based responses. Secondly, considering the clean nature of hydrogen, a diverse utilization model for hydrogen is established, including power-to-hydrogen, hydrogen-to-methane, hydrogen-to-heat/electricity, and blending hydrogen with natural gas. Lastly, by combining green certificate trading with carbon trading, a joint green certificate-carbon trading mechanism is proposed, and an IES low-carbon economic operation model that takes into account this joint trading mechanism is constructed. The simulation examples, which compare different operational scenarios, verify the effectiveness of the proposed model in enhancing renewable energy integration, improving energy utilization efficiency, and reducing carbon emissions.