We investigate the effect of a mirror-symmetry plane in multiple-scattering media under plane-wave illumination along the symmetry plane. Designed and fabricated samples' optical transport properties are compared quantitatively with three-dimensional modeling. Strong polarization-dependent deviations of the bulk speckle-averaged intensity distribution at the symmetry plane are observed, showing either up to a factor 2 enhancement or complete suppression of the ensemble-averaged intensities. We derive analytical expressions for the ensemble-averaged intensity profiles near the symmetry plane. Apart from their interest to fundamental light propagation studies, applications of mirror-symmetric scattering media are envisioned in anticounterfeiting.