Effects on the density of vibrational states due to the interface created between two types of solid Lennard-Jones systems is investigated as a function of the atomic masses and model potential parameters. The interface is responsible for a depletion of modes at low frequency and an enhancement at higher frequencies when the potential parameters are increased relative to the reference solid. Opposite trends are observed when the atomic mass increases. When a heat current is established across the interface the density of vibrational states at low frequency is increased and the temperature profile across the binary sample displays a discontinuity at the interface, which is more pronounced as the material parameters become more dissimilar. The thermal boundary resistance (Kapitza resistance) increases as the difference between the two material properties increases and decreases with increasing temperature. It is predicted that, as temperature decreases, the Kapitza length increases as T⁻² at the nanoscale. Plots of the thermal conductivity as a function of temperature for solids with various parameters are provided, all of them showing the expected T⁻¹ behavior.