We present a novel, to the best of our knowledge, form of polarization microscopy capable of producing quantitative optic-axis and phase retardation maps of transparent and anisotropic materials. The proposed method operates on differential phase-contrast (DPC) microscopy that produces a phase image of a thin specimen using multi-axis intensity measurements. For polarization-sensitive imaging, patterned illumination light is circularly polarized to illuminate a specimen. The light transmitted through a specimen is split into two orthogonal polarization states and measured by an image sensor. Subsequent DPC computation based on the illumination patterns, acquired images, and the imaging model enables the retrieval of polarization-dependent quantitative phase images, which are utilized to reconstruct the orientation and retardation of the specimen. We demonstrate the validity of the proposed method by measuring the optic-axis and phase retardation maps of calibrated and various anisotropic samples.