Following our earlier work [F. Flossmann et al., Phys. Rev. Lett. 95 253901 (2005)], we describe the fine polarization structure of a beam containing optical vortices propagating through a birefringent crystal, both experimentally and theoretically.We emphasize here the zero surfaces of the Stokes parameters in three-dimensional space, two transverse dimensions and the third corresponding to optical path length in the crystal. We find that the complicated network of polarization singularities reported earlier - lines of circular polarization (C lines) and surfaces of linear polarization (L surfaces) - can be understood naturally in terms of the zeros of the Stokes parameters.