Accurate prediction and control of heat dissipation across material interfaces is critical to the performance and reliability of advanced electronic devices. Classical models such as the diffuse mismatch model (DMM) cannot fully capture phonon dynamics. In this work, we solve the phonon Boltzmann transport equation (BTE) using an energy-based deviational Direct Simulation Monte Carlo (DSMC) method to calculate the interfacial thermal resistance (ITR) at a Silicon/Germanium interface. A quantum-informed interfacial boundary condition is developed by integrating the scattering matrix (S-matrix) from the atomistic Green's function framework, providing frequency- and polarization-resolved phonon transmission and reflection. This method captures detailed phonon dynamics at interfaces, and provides predictions of ITR that differ from the conventional DMM boundary condition, showing good agreement with experimental benchmarks. Transmission and specularity parameters extracted from the S-matrix model are further incorporated to refine the DMM method. We find that the modified DMM can provide similar results for ITR as the S-matrix for larger system sizes, but does not provide good agreement for smaller, nanoscale system sizes, where we expect the S-matrix to be more accurate. By integrating quantum insights with macroscopic modeling, this approach offers a practical tool for the engineering design of advanced electronic devices.