We present a universal technique for non-invasive diagnostics of thin multilayer optically-transparent tissues, based on the polarization-sensitive optical-coherence tomography. To reach higher diagnostic accuracy, we revisit the model of the cornea structure, and re-consider physical features of the interaction of light with the tissue structural elements. In the scheme proposed, the probing beam is algorithmically adjustable such that the x-polarized radiation impinges each consecutive structural layer; the object beam is formed by the reflection and back-scattering. Its characteristics are found analytically and numerically within the framework of the polarized Monte-Carlo model and the Jones matrix formalism. A modified Mach-Zehnder interferometer with orthogonal polarization channels enables to eliminate the object-signal depolarization caused by stochastic scattering, and facilitates evaluation of the refractive indices and bi-refringence of the tissue elements. The technique permits longitudinal (in depth) and transverse scanning of the object, providing a complete 3D mapping of the cornea structure.