Biomass, as one of the most accessible renewable resources, could reduce dependency on fossil fuels and mitigate associated environmental impacts. With economic development and improved living standards, biomass in rural areas is converted into various forms of energy to meet high energy demands. However, existing studies on rural multi-energy system operations assume energy production from biomass is a given input parameter and consider it to be a fixed constant or subject to upper and lower bounds, independent of the biomass supply chain. Indeed, biomass energy production is significantly influenced by the collection, transportation, storage, and other processes within the supply chain. This work proposes a mixed integer linear program (MILP) for the joint optimization of an integrated rural multi-biomass-solid waste energy conversion system with a source-grid-demand-based biomass-solid waste supply chain (IRMBS-BSC system). The IRMBS-BSC system encompasses three sub-systems: the biomass-solid waste source sub-system, the biomass-solid waste grid sub-system, and the biomass-solid waste demand sub-system. Various biomass-solid wastes are classified, and a source model is established to evaluate their availability. Subsequently, a supply chain model is developed within the biomass-solid waste grid sub-system. Based on the available and transported quantity from the biomass-solid waste source sub-system and grid sub-system, a multi-energy system operation model, considering refined biomass conversion processes, is proposed. A case study involving a multi-energy system that integrates multiple rural community biomass-solid waste supplies is conducted. The results demonstrate that the proposed MILP, which considers the biomass-solid waste supply chain, can reduce energy imports during the load peak periods and can also decrease the overall operational costs of the multi-energy system.