We develop an analytical theory that accounts for the image and surface charge interactions between a charged dielectric membrane and a DNA molecule translocating through the membrane. Translocation events through neutral carbon-based membranes are driven by a competition between the repulsive DNA-image-charge interactions and the attractive coupling between the DNA segments on the trans and the cis sides of the membrane. The latter effect is induced by the reduction of the coupling by the dielectric membrane. In strong salt solutions where the repulsive image-charge effects dominate the attractive trans-cis coupling, the DNA molecule encounters a translocation barrier of ∼10 kBT. In dilute electrolytes, the trans-cis coupling takes over image-charge forces and the membrane becomes a metastable attraction point that can trap translocating polymers over long time intervals. This mechanism can be used in translocation experiments in order to control DNA motion by tuning the salt concentration of the solution.