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New microscopic tight-binding model for calculation of charge transport in heterostructures containing unusual multiband materials is proposed. This approach allows to take into account multiband Fermi surface, the nonparabolic excitation spectrum of the considered materials and also interband and intervalley scattering at the boundaries. Our tight-binding approach has been applied to the investigation of the proximity effect in heterostructures, containing materials with strong spin-orbit interaction and topological insulators (for example, 3D strained HgTe). Induced superconducting order parameter in this material should not be treated the same as in the single-band metal due to its essentially multiband structure. Taking into account multiorbital structure and complex non-parabolic excitation spectrum in such interesting materials we have calculated the induced by usual s-wave superconductor excitation spectrum in them and have created a theoretical basis for the calculation of the normal and Josephson current in structures containing metals with strong spin-orbit interaction and three-dimensional topological insulators describing in the framework of multiorbital models.