The current–voltage characteristics (CVC) for nonstationary Josephson I¹, interference I², and quasiparticle J currents through tunnel junctions involving partially dielectrized superconductors with charge-density waves were calculated. The CVC peculiarities depend on combinations of superconducting, Δ, and dielectric, Σ, order parameters for both electrodes. Symmetrical (s) and nonsymmetrical (ns) junctions, when one of the electrodes is an ordinary (BCS) superconductor, are considered in detail. The current J_ns depends on the voltage polarity, which is not inherent to the ns-junctions involving only BCS superconductors. In the s-case, both symmetrical and nonsymmetrical CVC for J_s are possibly depending on the Σ equality (including their signs) for electrodes. The theory describes the properties of NbSe₃ and high-T_c oxides.