The accompanying exergy-cost-carbon nexus in trigeneration systems brings challenges to distinguishing the formation mechanisms of costs and carbon footprints of power, cold, and heat. In this paper, a fuel cell trigeneration system based on biomass gasification is constructed, and seven optional system configurations are designed according to the waste heat utilization methods including organic Rankine cycle, absorption cycle, and heat exchange. A novel exergy-based cost and carbon footprint model based on the energy levels of energy streams is proposed to obtain the allocation rules of multiple products of the trigeneration system, in which carbon cost with exergy cost is integrated into the exergo-economic method. Using this method, the coupling relationships of exergy-cost-carbon are illustrated and the unit exergy-carbon costs and carbon footprints of electricity, cold, and heat are determined. To select the optimum configuration, a multi-criteria decision-making method, considering energetic, economic, and environmental aspects, is employed to calculate their compositive scores, in which the integrated weights of indicators combine the experts’ knowledge and opinions with the entropy information of numerical performances of alternative trigeneration configurations. The sensitivities of exergy-cost and exergy-carbon performances on operation time, carbon footprint of biomass, and interest rate are implemented to discuss their influences. The consideration of energy level increases the cost and carbon footprint of power from fuel cells by around 30%. The carbon cost of system power, chilled water, and hot water account for 5.18%, 6.89%, and 5.25% of their corresponding total exergy-carbon costs. The integration of biomass gasification, fuel cell, gas turbine, and heat exchanger achieves the best comprehensive performance.