We present the derivation of boundary conditions on a wave function at the normal metal/superconductor (N/S) interface by extending the tight-binding approach developed for semiconducting heterostructures [Phys. Rev. 27 (1983) 3519]. Based on these boundary conditions, we formulate a quantitative theory for tunneling spectroscopy in N/S junctions, where a superconductor is characterized by complex non-parabolic energy spectrum beyond effective mass approximation. As an application to single-band unconventional superconductors, we re-derive the known conductance formula [Phys. Rev. Lett. 74 (1995) 3451] with generalized definition of a normal-state conductance. We further apply the model to junctions between normal metals (N) and multi-band iron-based superconductors (FeBS). Our calculations show that tunneling studies of (100) oriented N/FeBS junctions allow to distinguish between the and the order parameter symmetry in FeBS. In low transparent N/FeBS junctions with the symmetry in FeBS, finite energy subgap Andreev bound states are formed due to sign change of pair potential between different Fermi surface pockets. Another fingerprint of the symmetry in FeBS is suppressed Andreev conductance in high transparent (100) N/FeBS junctions compared to the case of the symmetry. Our results may serve as a basis for quantitative tunneling spectroscopy of FeBS.