Modeling charge transport across material interfaces is important for understanding the limitations of electronic devices such as transistors, electrochemical cells, sensors, and batteries. However, modeling the entire structure and full dimensionality of an interface can be computationally demanding. In this study, we investigate the validity of an efficient reduced one-dimensional Hamiltonian for calculating charge transport along interfaces by comparing to a two-dimensional model that accounts for additional charge transport pathways. We find that the one-dimensional model successfully predicts the qualitative trend of charge transmission probability among Pt/Fe2O3 and Ag/Fe2O3 interfaces. However, the two-dimensional model provides additional information on possible pathways that are not perpendicular to the interface direction. These charge transport pathways are directed along the lowest potential energy profile of the interface that correlates with the crystal structure of the constituting materials. However, the two-dimensional paths are longer and take more scattering time. Therefore, the one-dimensional model may hold sufficient information for qualitative estimation of charge transport through some material interfaces.