The condensed phases of phospholipid monolayers on an air/water interface are described by means of a microscopic interaction model which incorporates intra-chain flexibility as well as crystal orientation variables. The phase transitions and microstructures are studied as functions of lateral pressure. The model predicts, in accordance with recent synchrotron X-ray experiments, that the chain-ordering transition and the crystallization of the monolayer need not take place at the same lateral pressure.