A theoretical model describing the formation and shapes of domains in amphiphilic monolayers driven by screened electrostatic interactions is presented. The model is related to previous studies of pattern formation in magnetic systems in Hele-Shaw cells. Using quantitative estimates of line tension, charge density, and ionic strength appropriate for biological systems, this model accounts for the appearance of circular and irregular domains in mixed, lipid monolayer systems containing the anionic lipid phosphatidylinositol monophosphate. The results may have implications for pattern formation in both, synthetic materials and biological membranes.