In this manuscript, we develop a generalized theory for the scattering process produced by interface roughness on charge carriers that is suitable for any semiconductor heterostructure. By exploiting our experimental insights into the three-dimensional atomic landscape of heterointerfaces obtained by atom probe tomography, we are able to define the full set of interface parameters relevant to the scattering potential, including both the in-plane and axial correlation inside real diffuse interfaces. Our experimental findings indicate a partial coherence of the interface roughness along the growth direction within the interfaces. We show that it is necessary to include this feature, previously neglected by theoretical models, when heterointerfaces characterized by finite interface widths are taken into consideration. To show the relevance of our generalized scattering model in the physics of semiconductor devices, we implement it in a nonequilibrium Green’s function simulation platform to assess the performance of a -based terahertz quantum cascade laser.