Interfacial structures of c-axis-oriented YBa2Cu3O7–y (Y123) and Nd1+xBa2–xCu3O7–y (Nd123) films were investigated by high-resolution transmission electron microscopy (HRTEM) in conjunction with geometrical lattice matching and molecular orbital calculations. These films were formed on MgO(001) substrates by liquid-phase epitaxy. Despite the similarity in lattice constants between Y123 and Nd123, the in-plane orientation relationship (OR) to the substrates is different: film//substrate(I) for Y123 and film//substrate(II) for Nd123. From the results of HRTEM observations and image simulations, it was found that the Y123 and Nd123 films are terminated by BaO and CuO-chain layers at the interfaces, respectively. For both the Y123/MgO and Nd123/MgO systems, the OR(I) is assessed to be the most favorable in point of geometrical matching and the OR(II) is the second among the rotational misorientations on the film and MgO. The molecular orbital calculations reveal that the interface with the OR(II) and the CuO-chain layer termination is preferable in terms of covalent bonding for both the systems. Consequently, we suggest that the preferential interfacial structures are delicately determined by a balance of the geometrical and chemical factors at the interfaces, resulting in making the lowest interfacial free energies.