We study superconductor-insulator layered structures, using a microscopic method based on the Gorkov equations. We present our results for the single-particle density of states and the order parameter (OP) as a function of the experimental parameters, such as the insulating barrier strength, the coherence length, and the range of transverse momentum of probes. The results provide a very good fit to the tunneling spectra of Bi2Sr2CaCu2O8, obtained in a soft-point-contact scanning-tunneling microscopy measurement. The results also indicate that the OP in strongly coupled superconducting regions (such as CuO planes in high-temperature superconductors), may be significantly larger than the energy gap found in experiments. The role of all relevant physical and geometrical parameters is also discussed.