We introduce a microscopic model of a lipid with a charged headgroup and flexible hydrophobic tails, a neutral solvent, and counter ions. Short-ranged interactions between hydrophilic and hydrophobic moieties are included as are the Coulomb interactions between charges. Further, we include a short-ranged interaction between charges and neutral solvent, which mimics the short-ranged, thermally averaged interaction between charges and water dipoles. We show that the model of the uncharged lipid displays the usual lyotropic phases as a function of the relative volume fraction of the headgroup. Choosing model parameters appropriate to dioleoylphosphatidylethanolamine in water, we obtain phase behavior that agrees well with experiment. Finally we choose a solvent concentration and temperature at which the uncharged lipid exhibits an inverted hexagonal phase and turn on the headgroup charge. The lipid system makes a transition from the inverted hexagonal to the lamellar phase, which is related to the increased waters of hydration correlated with the increased headgroup charge via the charge-solvent interaction. The polymorphism displayed upon variation of pH mimics that of the behavior of phosphatidylserine.