As the global energy structure undergoes transformation and the low-carbon development process continues to advance, integrated energy systems have progressively emerged as crucial technical support for achieving sustainable development. In this paper, a joint-day optimal scheduling model is put forward considering the existence of dispatchable resources in community integrated energy systems (CIES). The aim is to cut down the system operation cost and enhance energy utilization efficiency. This model is founded on the concept of energy hubs and combines the shiftable, transferable, and reducible characteristics of demand-side flexible loads. It includes gas turbine power generation systems, energy storage, as well as wind and solar renewable resources. System operation cost and carbon trading cost are comprehensively taken into account, and ultimately, the CIES low-carbon economic dispatch model with the lowest total cost as the optimization objective is established. The Yalmip toolbox and Cplex solver are employed to solve the model. The optimization results of flexible electric and thermal loads participating in dispatching under different scenarios are analyzed through simulation. The economic benefits of electric and thermal independent dispatching are compared and analyzed, and the economic benefits of electric and thermal coupled dispatching are verified. The study reveals that the rational scheduling of user-side flexible loads can notably reduce operating costs, lower the load peak-to-valley difference and carbon emissions, and boost the comprehensive economic and environmental benefits of the system.