In the regional integrated energy system (RIES) with multi-participation of user side, supply side, and integrated energy retailer (IER), the interaction and collaboration among various participants in a multi-energy trading mode are difficult to reveal under the conventional vertical integrated structure, which poses challenges to achieve an economical and low-carbon operation of RIES. This paper proposes a cloud-edge cooperative framework-based electricity-heat collaborative optimization strategy to address this issue. The multi-energy trading considering carbon trading process is embedded within the cloud-edge coordination framework, where IER is considered as the cloud side. In contrast, the user and supply sides are considered the edge sides, and the success-history-based adaptive differential evolution (SHADE) algorithm is adopted to obtain the interaction strategy. The simulation demonstrates that compared to the conventional vertical integrated structure, the RIES’s carbon emissions have decreased by 2.4% and transaction costs have decreased by 3.4%.