Directly coupled hard and soft ferromagnets were popularly used as the hybridized electrodes to enhance tunnel magnetoresistance (TMR) ratio in the perpendicular magnetic tunnel junction (pMTJ). In this paper, we employ the density functional theory (DFT) with general gradient approximation (GGA) to investigate the interfacial structure and magnetic behavior of tetragonal Heusler-type MnGa (MG)/L21-Co2MnSi (CMS) Heusler alloy bilayers with the MnGa being D022-MnGa alloy (Mn3Ga) and L10-MnGa alloy (MnGa). The MM-MS_B interface with the bridge (B) connection of MnMn termination (MM) of D022- and L10-MnGa layers to MnSi termination (MS) of CMS layers is found to be most stable in the energy point of view. Also, a strong antiferromagnetic coupling and relatively higher spin polarization can be observed in the MM-MS_B interface. Further, a remarkable potential difference to derive electrons to transfer from MG layer to CMS layer appears at the interface. These theoretical results indicate that the MG/CMS bilayers are promising candidates as coupled composites, and moreover, the D022-MG/CMS bilayer is better than L10-MG/CMS bilayer due to its larger spin polarization and built-in field at the interface.