We have performed a detailed study of the effect of the HTS degraded surface layer on conductance spectra of HTS/metal junctions. It has been found that the corresponding resistance changes by applying an external bias voltage can be explained as an alteration of the oxygen content near the interface. To take into account the spatially inhomogeneous nature of a few top HTS unit cells, we have examined theoretically the influence of a nonuniform normal covering on the subgap tunneling characteristics of a superconductor. A simple approach to coherent charge transport through a planar double-barrier structure has been generalized to the case of an anisotropic order parameter, non-uniformity of the middle nonsuperconducting layer, and magnetic field effect. In particular, we show that, under suitable circumstances, the conductance peak at zero bias voltage and its splitting at low temperatures often observed for HTS/metal junctions can be interpreted within the s-wave scenario, too, if above mentioned inhomogeneity is considered.