Two-dimensional (2D) B-C compounds possess rich allotropic structures with many applications. Obtaining new 2D B4C3 structures is highly desirable due to the novel applications of three-dimensional (3D) B4C3 in protections. In this work, we proposed a new family of 2D B4C3 from the first-principles calculations. Distinct from previous observations, this family of 2D B4C3 consists of bonded 2D B4C3 bilayers. Six different types of bilayers with distinct bonded structures are found. The phonon spectrum calculations and ab initio molecular dynamics simulations at room temperature demonstrate their dynamic and thermal stabilities. Low formation energies suggest the high possibility of realizing such structures in experiments. Rich electronic structures are found, and the predicted Young's moduli are even higher than those of the previous ones. It is revealed that the unique electronic and mechanical properties are rooted in the bonding structures, indicating the prompting applications of this family of 2D B4C3 materials in photovoltaics, nanoelectronics, and nanomechanics.