In remote power station camps without access to centralized heating networks, developing an economic, stable, and reliable heating solution is essential. This study proposes a multi-energy complementary heating system (MECH) integrating solar collectors, an air source heat pump, and an electric boiler. An energy balance equation is established for the system, and a multi-objective optimization method based on NSGA-II and TOPSIS is applied to minimize the levelized cost of heating (LCOH) and annual carbon emissions. The results indicate that a solar collector area of 1588 m2, along with rated heating capacities of 38 kW for the air source heat pump and 16 kW for the electric boiler, effectively meets the heating demands. Under this configuration, the LCOH is approximately 0.218 CNY/kWh, and annual CO₂ emissions are approximately 1.48 × 105 kg. Compared to the initial air source heat pump-electric boiler heating system, the proposed MECH reduces the initial investment, LCOH, and carbon emissions by 9.76%, 31.01%, and 37.78%, respectively. This study provides a reference for designing efficient MECH for power station camps in remote regions.