Detailed knowledge of neutrino transport properties in matter is crucial for an understanding of the evolution of supernovae and of neutron star cooling. We investigate screening of neutrino scattering from a dense degenerate gas of electrons, protons and neutrons. We take into account correlations induced by the Coulomb interactions of the electrons and protons, and the strong interactions of the protons and neutrons. Nuclear matter is described by the sigma-omega-model of quantum hadrodynamics. Results are presented for typical astrophysical scenarios. The differential cross section is strongly reduced at large energy transfer, where electrons dominate, and slightly reduced for small energy transfer, where nucleons dominate. At large densities, the nucleon effective mass is considerably lower than the free mass, and the region dominated by nucleons extends to larger energy transfer than for free nucleons.