We have theoretically investigated the modeling and the structural stabilities of various Mg/MgH2 interfaces, i.e. Mg($10\bar 10$101¯0)/MgH2(210), Mg(0001)/MgH2(101) and Mg($10\bar 10$101¯0)/MgH2(101), and provided illuminating insights into Mg/MgH2 interface. Specifically, the main factors, which impact the interfacial energies, are fully considered, including surface energies of two phases, mutual lattice constants of interface model, and relative position of two phases. The surface energies of Mg and MgH2, on the one hand, are found to be greatly impacting the interfacial energies, reflected by the lowest interfacial energy of Mg(0001)/MgH2(101) which is comprised of two lowest energy surfaces. On the other hand, it is demonstrated that the mutual lattice constants and the relative position of two phases lead to variations of interfacial energies, thus influencing the interface stabilities dramatically. Moreover, the Mg-H bonding at interface is found to be the determinant of Mg/MgH2 interface stability. Lastly, interfacial and strain effects on defect formations are also studied, both of which are highly facilitating the defect formations. Our results provide a detailed insight into Mg/MgH2 interface structures and the corresponding stabilities.