As an efficient form of energy utilization, an integrated energy system integrates oil, natural gas, coal, and other energy sources and converts them into electric, cooling, and heating for users through energy conversion devices. In this process, integrated energy service providers need to make energy conversion decisions based on users’ demand information feedback. Therefore, there is uncertainty and coupling between the electric cooling and heating loads, making it difficult to forecast the loads accurately. Firstly, this paper analyzes the integrated energy system’s energy consumption characteristics and the interaction mechanism between the supply and demand sides, which fundamentally explains the coupling relationship between different loads of the integrated energy system. Secondly, REC, DEC, REH, and DEH are constructed from electric cooling and heating loads. The relationship between electric load and cooling and heating load is analyzed by a scatter distribution diagram and maximum information coefficient method. The nonlinear correlation between electric load and cooling and heating loads is proved. Based on this, the integrated energy system’s synergetic electric load forecasting formula reflecting the nonlinear synergistic effect between loads is proposed. Finally, based on stacking ensemble learning, an integrated energy system electric load forecasting model considering the nonlinear synergy between loads is established by integrating BP neural network, support vector regression, random forest, and gradient boosting decision tree. Through the experimental analysis of the Arizona State University Tempe campus’s integrated energy system project, it is found that the effect of the synergistic quadratic forecasting is better than that of the primary forecasting. Besides, the MAPE of the quadratic synergistic forecasting formula is lower than that of the other two forms, indicating that the proposed synergistic electric load forecasting formula considering the nonlinear synergy between loads can improve the accuracy of electric load forecasting of the integrated energy system.