This study develops a novel mathematical modelling framework for biomass combined heat and power systems (CHP) linking physicochemical/thermodynamic characteristics and life cycle sustainability. A total of twenty-nine indicators for the process (4), economic (5), environmental (8) and social global (5) and local (7) aspects have been analysed for sustainability. These are biomass throughput, electricity and steam generations and CHP efficiency; internal rate of return, capital, operating and feedstock costs and cost of production; global warming, fossil, land and water use, acidification, urban smog, eutrophication and ecotoxicity potentials; labour rights & decent work, health & safety, human rights, governance and community infrastructure; total forest land, direct/indirect jobs, gender equality and energy-water-sanitation access for communities, from biomass characteristics (carbon and hydrogen contents), energy demands and economic parameters. The model is disseminated as an open-web-resource https://tesarrec.web.app/sustainability/chp. In a case study approach, from 12.47 kt/year forestry residue, 1 MWe is generated with an associated low-pressure steam generation of 50 kt/year, at a cost of production of $0.023/kWh, making “affordable and clean energy” (the UN Sustainable Development Goals, SDG7) for marginalised/poor communities. Bioenergy can curb >90% greenhouse gas emissions and primary energy, 6 kt CO2 eq and 74 TJ annually, 87-53% water consumption, acidification and eutrophication, and 29-18% urban smog and ecotoxicity, compared to fossil-based counterpart. All five social themes in the Central American cluster countries can be improved by bioenergy. In addition to SDG7, SDG6: "clean water and sanitation for all" can be delivered by forestry-based bioenergy system.