Two-dimensional in-plane interface structures of highly epitaxial perovskite (La,Ca)MnO3 (LCMO) and (Pb,Sr)TiO3 (PSTO) thin films on salt-rock type MgO substrate were studied using Transmission Electron Microscopy (TEM). Cross-section TEM studies revealed that both LCMO and PSTO films are good single crystal quality and have atomic sharp interface with respect to the MgO substrate with -6.4% and -6.2% lattice mismatch, respectively. Electron Diffraction Patterns (EDPs) of plan-view LCMO/MgO and PSTO/MgO interfaces exhibit double diffraction spots. An analytical approach was employed using double diffraction to study the two-dimensional in-plane interfaces of perovskite structure films on the salt-rock type substrate. The lattice mismatch near the interface regions was determined using EDPs of the plan-view interfaces and found to be -8.0% for LCMO/MgO and -7.14% for PSTO. Both latter values are larger than those obtained using cross-section TEM. Studies of the sharpness of double diffraction spots and plan-view high resolution (HR) TEM brought a conclusion that the PSTO film is well commensurate with the MgO substrate over large areas, whereas LCMO film is only locally commensurate with the substrate. These studies provide additional evidence to our previous observations that plan-view TEM of the interface is able to provide critical and valuable information that is lacking from the cross-section TEM analysis.