A variety of superconducting materials exhibit multi-band behavior in a form of multicomponent Fermi surfaces. By using a two-band model with a pair hopping, we explain how the interband coupling affects the physical properties of multi-band superconductors. We determine the temperature dependence of the superconducting gap and the specific heat, which strongly diverge from the BCS-type behavior. The anisotropic gap for the system with the mixed gap symmetry is found. Additionally, the spectral function and density of states are significantly modified by the inter-orbital interactions. The results obtained for different symmetries of the order parameter are in a good agreement with the experimental findings for the iron-based superconductors and other multi-band systems.