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The propagation of acoustic waves through interface of two crystals is studied on microscopic level using the discrete lattice model. The phonon transmission through the intercalated layer between two semi-infinite lattices is considered. The general expressions for energy fluxes and impedances are proposed. The resonance transmission of phonons through the interface of the 3D pressure made Si-Cu point contact was studied using the discrete model of the crystal lattice. We show that anomalous behavior of the reduced heat flux in the temperature range 1 K < T < 25 K are induced by the resonance transport of phonons through the layer of impurity atoms. The data obtained are in a good agreement with the experimental results.