The organization of fibrillar tissue on the micrometer scale carries direct implications for health and disease but remains difficult to assess in vivo. Polarization-sensitive optical coherence tomography measures birefringence, which relates to the microscopic arrangement of fibrillar tissue components. Here, we demonstrate a critical improvement in leveraging this contrast mechanism by employing the improved spatial resolution of focus-extended optical coherence microscopy (1.4 µm axially in air and 1.6 µm laterally, over more than 70 µm depth of field). Vectorial birefringence imaging of sheep cornea ex vivo reveals its lamellar organization into thin sections with distinct local optic axis orientations, paving the way to resolving similar features in vivo.