We reexamine the problem of charge renormalization and inversion of a highly charged surface of a low dielectric constant immersed in ionic solutions. To be specific, we consider an asymmetrically charged lipid bilayer, in which only one layer is negatively charged. In particular, we study how dielectric discontinuities and charge correlations (among lipid charges and condensed counterions) influence the effective charge of the surface. When counterions are monovalent (e.g., Na+), our mean-field approach implies that dielectric discontinuities can enhance counterion condensation. A simple scaling picture shows how the effects of dielectric discontinuities and surface-charge distributions are intertwined: Dielectric discontinuities diminish condensation if the backbone charge is uniformly smeared out while counterions are localized in space; they can, however, enhance condensation when the backbone charge is discrete. In the presence of asymmetric salts such as CaCl2 , we find that the correlation effect, treated at the Gaussian level, is more pronounced when the surface has a lower dielectric constant, inverting the sign of the charge at a smaller value of Ca2+ concentration.