An experimental implementation of the nonlinear Stokes-Mueller polarimetric (NSMP) microscopy in third-harmonic generation modality is presented. The technique is able to extract all eight 2D-accessible χ(3) components for any sample from 64 polarization measurements, and can be applied to noninvasive ultrastructural characterization. The polarization signature of an isotropic glass coverslip is presented, and carotenoid crystallites in the root of orange carrot (Daucus carota) are investigated, showing complex χ(3) components with a significant chiral contribution.