The epoxy-bonded joint between carbon-fiber-reinforced bismaleimide (CF-BMI) and quartz-fiber-reinforced bismaleimide (QF-BMI) composites can meet the structure–function integration requirements of next-generation aviation equipment, and the structural design of their bonding zones directly affects their service performance. Hence, in this study, the carbon-fiber-reinforced bismaleimide composite ZT7H/5429, the woven quartz-fiber-reinforced bismaleimide composite QW280/5429, and epoxy adhesive film J-116 were used as research materials to investigate the influence of the bonding area size on the mechanical properties, and this study proposes a novel design methodology combining radial basis function (RBF) neuron machine learning with the NSGA-II algorithm to enhance the mechanical properties of the bonded components. First, a finite element simulation model considering 3D hashin criteria and cohesion was established, and its accuracy was verified with experiments. Second, the RBF neuron model was trained using the finite element tensile strength and shear strength data from various adhesive layer parameter combinations. Then, the multi-objective parameter optimization of the surrogate model was accomplished through the NSGA-II algorithm. The research results demonstrate a high consistency between the finite element simulation results and experimental outcomes for the epoxy-bonded CF/QF-BMI composite joint. The stress distribution of the adhesive layers is similar under the different structural parameters of adhesive films, though the varying structural dimensions of the adhesive layers lead to distinct failure modes. The trained RBF neuron model controls the prediction error within 2.21%, accurately reflecting the service performance under various adhesive layer parameters. The optimized epoxy-bonded CF/QF-BMI composite joint exhibits 16.1% and 11.2% increases in the tensile strength and shear strength, respectively.