To reduce the carbon emissions from the hydrocracking unit in refinery, this work proposes the coupling of bio-oil co-processing technology with green hydrogen and green electricity in the hydrocracking unit. However, the higher costs associated with biomass feedstock, green hydrogen, and green electricity result in an elevated overall cost for this process. To investigate the relationship between economic costs and carbon emissions in the co-processing hydrocracking unit with coupled green hydrogen and green electricity, a multi-objective optimization model is introduced, targeting to minimize total cost and carbon emissions simultaneously. Three scenarios are proposed for better comparison under different objectives: the minimum cost scenario, minimum carbon emissions scenario, and trade-off scenario. The minimum cost scenario incurs a total cost of only 15,494.1 MRMB/y (million Renminbi per year, currency in China), but with a high emission of 5.95 Mt CO2/y. The minimum carbon emissions scenario results in costs and emissions of 20,421.9 MRMB/y and 4.97 Mt CO2/y, respectively. The trade-off scenario yields cost and carbon emission values of 15,580.9 MRMB/y and 5.76 Mt CO2/y. Furthermore, sensitivity analysis reveals that the co-processing ratio of bio-oil has the most substantial influence on the overall process. The proposed model and results provide a theoretical foundation for the design and optimization of the co-processing hydrocracking unit.