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Understanding the interfaces in heterostructures at an atomic scale is crucial in enabling the possibility to manipulate underlying functional properties in correlated materials. This work presents a detailed study on the atomic structures of heterogeneous interfaces in La_0.7Sr_0.3MnO₃ (LSMO) film grown epitaxially on c-Al₂O₃ (0001) with a buffer layer of MgO. Using aberration-corrected scanning transmission electron microscopy, we detected nucleation of periodic misfit dislocations at the interfaces of the large misfit systems of LSMO/MgO and MgO/c-Al₂O₃ following the domain matching epitaxy paradigm. It was experimentally observed that the dislocations terminate with 4/5 lattice planes at the LSMO/MgO interface and with 12/13 lattice planes at the MgO/c-Al₂O₃ interface. This is consistent with theoretical predictions. Using the atomic-resolution image data analysis approach to generate atomic bond length maps, we investigated the atomic displacement in the LSMO/MgO and MgO/c-Al₂O₃ systems. Minimal presence of residual strain was shown at the respective interface due to strain relaxation following misfit dislocation formation. Further, based on electron energy-loss spectroscopy analysis, we confirmed an interfacial interdiffusion within two monolayers at both LSMO/MgO and MgO/c-Al₂O₃ interfaces. In essence, misfit dislocation configurations of the LSMO/MgO/c-Al₂O₃ system have been thoroughly investigated to understand atomic-scale insights on atomic structure and interfacial chemistry in these large misfit systems.