We study the electrostatic properties of discrete charges at an electrolyte-insulator interface. The associated counterion cloud comprises, besides the exponential Debye screening, an algebraic tail with an amplitude that depends on the dielectric constant epsilon(ins), Of the insulator. For very thin electrolyte films, the counterions spread to large distances well beyond the Debye length. At low surface charge density, the disjoining pressure of a thin film is dominated by single-charge effects and depends on epsilon(ins).