In this work, we investigate the phase stability, electronic structure, and superconducting properties of the two-dimensional ternary borocarbides MB₄C₂ (M = Ca, Mg) using first-principles calculations and fully anisotropic Migdal-Eliashberg theory. Ab initio molecular dynamics, phonon dispersion, and elastic constant calculations confirm that both monolayers are dynamically, thermally, and mechanically stable. Electronic structure analysis reveals an intrinsic metallic nature with a multiband Fermi surface, where states near the Γ point are dominated by in-plane B-pₓ, p_y orbitals, while zone-boundary states are primarily derived from out-of-plane B-p_z orbitals. The electron-phonon coupling is determined to be λ = 0.64 for both materials, driven by the rigid covalent B-B and B-C honeycomb networks. By solving the anisotropic Eliashberg equations, we predict that CaB₄C₂ and MgB₄C₂ are nodeless two-gap superconductors with critical temperatures (T_c) of 33.4 K and 33.8 K, respectively, at a Coulomb pseudopotential of μ = 0.10. Furthermore, the superconducting state remains robust under increased Coulomb repulsion (μ = 0.13), retaining elevated T_c values of 31.2 K and 30.9 K, respectively. These findings establish MB₄C₂ monolayers as promising candidates for nanoscale superconducting applications and enrich the family of two-dimensional multigap superconductors.