Under the background of carbon neutrality, efficient and low-carbon cooling and heating in rural areas away from the centralized network is a meaningful topic. In this paper, a multi-energy complementary absorption system is proposed to provide space heating in winter and cooling in summer. The system utilizes renewable energy that is abundant in rural areas, including solar and biomass, and balances the energy supply through natural gas replenishment. By adopting the cooling/heating medium circulation, multiple sets of indoor terminals are driven by a single set of absorption machine and outdoor unit. It is found that as long as the renewable energy ratio is higher than 0.2, the economic performance of the proposed system will be outstanding over the existing methods. When applied in Beijing, the annual operating cost for a typical household is reduced by 25.5–46.8% compared with traditional gas furnace/compression heat pump combined with air conditioner. Moreover, even when the proposed system is driven solely by natural gas, the carbon emission is reduced by 16–20% compared with traditional methods. When the renewable energy ratio is 0.4, the carbon reduction ratio reaches 41–44%, and the annual carbon emission for cooling and heating of a typical household reduces below 3000 kg. It is expected that by solving the problem of load and concentration variation during the year-round operation, the proposed system has great application potential in cold winter and hot summer areas away from the centralized cooling or heating network.