With the gradual transformation of the integrated energy system towards intelligence, cleanliness, and decentralization, an integrated power producer and consumer has emerged. To realize the full consumption of renewable energy and improve the interactive benefits of each subject, an electricity-and-heat trading strategy of the community integrated energy system based on a three-layer game is proposed. First, a master-slave game model of integrated energy operators and communities based on the nested community cooperation game is developed. Operators set time-of-use electricity and heat tariffs to maximize their benefits and pass them on to the energy community. Responding to the operators’ electric and thermal decisions, the energy community develops interaction strategies with other communities to maximize the consumption surplus, and determining and transferring the energy purchase demand to the operator. Secondly, to reduce carbon emissions and fully use the surplus resources of each operator, a Nash negotiation model for multiple integrated energy operators is established. The model is transformed by the Karush-Kuhn-Tucker (KKT) condition and convex relaxed by the McCormick method. Finally, the model is analyzed using an alternating direction multiplier distributed algorithm. The simulation verifies result that the proposed strategy can effectively optimize the interaction efficiency of each subject and reduce the carbon emission of the integrated energy system, improving the benefits for all subjects.