Combined cooling, heating, and power (CCHP) systems are a promising energy-efficient and environment-friendly technology. However, their performance in terms of energy, economy, and environment factors depends on the operation strategy. This paper proposes a multi-energy complementary CCHP system integrating renewable energy sources and schedulable heating, cooling, and electrical loads. The system uses schedulable loads instead of energy storage, at the same time, a collaborative optimization scheduling strategy, which integrates energy supply and load demand into a unified optimization framework to achieve the optimal system performance, is presented. Schedulable cooling and heating load models are formulated using the relationship between indoor and outdoor house temperatures. A genetic algorithm is employed to optimize the overall performance of energy, economy, and environment factors and obtain optimal day-ahead scheduling scheme. Case studies are conducted to verify the efficiency of the proposed method. Compared with a system involving thermal energy storage and demand response (DR), the proposed method exhibits a higher primary energy saving rate, greenhouse gas emission reduction rate, and operation costs saving rate of 7.44%, 6.59%, and 4.73%, respectively, for a typical summer day, thereby demonstrating the feasibility and superiority of the proposed approach.