Among various models for estimating interfacial thermal conductance (ITC) across different material interfaces, the diffuse mismatch model (DMM) has been generally evaluated as a reliable approach for material interfaces at high temperatures. The previous works by DMM have indicated the correct order of magnitude of ITC in isotropic material interfaces. However, it cannot accurately reproduce the ITC for low-dimensional anisotropic layered materials that are desired for many potential applications. Also, the inappropriate mode matching process approximation of the phonon dispersion curve tends to overestimate the ITC. In this paper, we revisited and updated the numerical method in our previous work that utilizes a mode-to-mode comparison within the DMM framework to predict ITC with the first-principles accuracy. We employed this model to calculate ITCs between layered materials such as MoS2 and graphite and metals such as Al, Au, and Cr. We then compared our values with previous literature data from calculations of phonon dispersion curve and experimental data from time-domain thermoreflectance measurements. With a better mode matching algorithm, the updated numerical method can predict the ITCs with improved accuracy. Further analysis also confirmed that counting only the three acoustic modes and neglecting the low-frequency optical modes lead to significant underestimation of the ITC using DMM.