The MINERvA Collaboration reports a novel study of neutrino-nucleus charged-current deep inelastic scattering (DIS) using the same neutrino beam incident on targets of polystyrene, graphite, iron, and lead. Results are presented as ratios of C, Fe, and Pb to CH. The ratios of total DIS cross sections as a function of neutrino energy and flux-integrated differential cross sections as a function of the Bjorken scaling variable x are presented in the neutrino- energy range of 5-50 GeV. Based on the predictions of charged-lepton scattering ratios, good agreement is found between the data and prediction at medium x and low neutrino energy. However, the ratios appear to be below predictions in the vicinity of the nuclear shadowing region, x < 0.1. This apparent deficit, reflected in the DIS cross-section ratio at high E., is consistent with previous MINERvA observations [B. Tice et al. (MINERvA Collaboration), Phys. Rev. Lett. 112, 231801 (2014).] and with the predicted onset of nuclear shadowing with the axial-vector current in neutrino scattering.