Considering the ambitious “dual carbon” targets set by China, it is imperative to develop an effective carbon trading framework. This framework should enhance the advantages of a low-carbon economy within an integrated energy structure, while effectively organizing the allocation of assets based on consumer demands, which are essential hurdles we need to overcome today. To tackle contemporary energy challenges, this research introduces a framework focused on enhancing the management of an energy infrastructure, facilitating the transformation from electricity to gas while incorporating carbon capture technologies in relation to adaptive energy demands. Initially, a framework is established that merges low-carbon technologies with storage and generation components within a multi-energy supply system. In addition, a novel carbon trading approach is presented to effectively monitor emissions within the system. Lastly, a scheduling plan is formulated, factoring in flexible resources from the demand side, where the objective function encompasses various cost elements. Through the comparison of scenarios, this approach shows its strong capability to minimize expenses and lower greenhouse gas release in the framework.