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Investigations of the charge transport in contacts with unusual superconductors allows to obtain the crucial information about the type of symmetry of the order parameter in them. Type of the symmetry of the order parameter in unusual superconductor sheds light on the type of superconducting pairing in them. Many new unusual superconductors, such as Fe-based superconductors (FeBS), Sr2RuO4, doped superconducting insulators CuxBi2Se3, are multibands metals with several bands, which intersect their Fermi surface. However, there is currently no consistent theory of coherent charge transport in contacts with them. In this paper, we present a consistent microscopic theory of charge transport in contacts of multiband superconductors with a normal metal and a usual s-type superconductor and break junctions. In our calculations we for the first time take into account crystal structure of multiband superconductors, the size of the Fermi surfaces, sign-changing and anisotropy of the order parameter, the misorientation angle of the boundary, as well as interband and intervalley scattering at the interface. Our general theory we apply to a specific analysis of the charge transport in contacts with FeBS, described by the two-orbital model, with a possible s++, s+- symmetry of the order parameter in them. As a result of microscopic calculations, we demonstrated the ability to distinguish between the symmetry of the order parameter in FeBS in above-listed tunneling experiments. We demonstrate that in experiments on tunneling transport in Sp-I-N (FeBS-Insulator-Normal metal) contacts it is necessary to use contacts with transport in the a-b plane with zero angle of misorientation and a large Fermi surface of a normal metal (N) [1]. In such experiments s++ and s+- symmetry of the order parameter in FeBS can be distinguished by the presence or absence of undergap features. In Josephson experiments to distinguish the symmetry of the order parameter of FeBS should be used S-I-Sp (usual s-type Superconductor-Insulator-FeBS) contacts with transport in c direction with a large Fermi surface of usual s- type superconductor (S). We demonstrate that it is necessary to investigate the difference between current-phase relations of S-I-Sp Josephson junctions with and without long oxide layer. We demonstrate that in order to distinguish the symmetry of the order parameter in FeBS it is necessary to investigate break junctions with transport the a-b plane. The suggested approach can be applied for the theoretical investigation of current transport in structures with mysterious Majorana fermions.