With the increasing demand side energy consumption, residential users have generated a large amount of carbon emissions from energy consumption, which has great potential for emission reduction. This article focuses on the low-carbon economic operation of community comprehensive energy systems, considering the linkage between energy and carbon prices, and establishes a low-carbon interactive management strategy for comprehensive energy systems based on real-time carbon intensity assessment. Firstly, a community comprehensive energy system architecture was established, and based on this, a residential carbon emission measurement method considering equivalent carbon emission reduction was proposed. Secondly, design a low-carbon demand response mechanism based on real-time carbon intensity assessment, guiding users to achieve carbon reduction and new energy consumption through multi energy complementarity. Then, a comprehensive energy system supply side scheduling model and a user side response model were established, achieving low-carbon economic operation through multi energy coupling and supply-demand interaction on both sides of supply and demand. Finally, the proposed real-time carbon intensity assessment mechanism was validated through simulation to effectively reduce carbon emissions from integrated energy systems.