In rural energy supply, combined heat and power (CHP) systems play a crucial role. These systems, however, are characterized by their complex internal structure and interdependencies among different energy sources. Additionally, their multifaceted objectives present significant optimization challenges. This study delves into rural energy supply CHP systems, considering photovoltaic and wind power generation, as well as the utilization of biogas digesters. Notably, the optimization process extends beyond mere economic considerations. It also incorporates demand-side responses, proposing corresponding compensation mechanisms. Furthermore, the cost analysis accounts for tiered carbon emission costs, aiming not only for economic optimization but also overall carbon emission reduction. To address the intricate goals, the study constructs a comprehensive model that considers load transfer for electricity, compensation for thermal loads, and response attenuation. The proposed optimization model effectively reduces costs, enhances system flexibility, and promotes environmentally friendly economics. By striking this balance, we can achieve sustainable energy solutions that benefit both the environment and the economy.