Recently Corvera, Laradji, and Zuckermann (unpublished) showed that the multistate lattice model due to Pink, Green, and Chapman [Biochemistry 20, 6692 (1981)] with parameters obtained from fitting to thermodynamic data for saturated phospholipid bilayers does not exhibit a phase transition but could instead be described in terms of short-range fluctuations close to a critical point. We have extended the Pink-Green-Chapman model by including hydrophobic mismatch interactions between the lipid acyl-chain conformational states. We used Monte Carlo techniques to examine the phase behavior of the extended model and found that it exhibits first-order phase transitions above a critical value of the mismatch parameter. The results are discussed in relation to previous theoretical work as well as experimental measurements on lipid bilayers.