Monte Carlo techniques have been applied to a study of two related quasi-two-dimensional microscopic interaction models which describe the phase behavior of phospholipid bilayers. The two models are Ising-like lattice models in which (a) the acyl chains of the phospholipids interact via anisotropic van der Waals forces and (b) the rotational isomerism of the chains is accounted for by two and ten selected conformational states, respectively. Monte Carlo experiments are performed on both models so as to determine whether the static thermodynamic properties of lipid bilayers are most accurately represented by a simple two state gel-fluid concept or whether a more complicated melting process involving intermediate states takes place. To this purpose, the temperature dependence of several static thermodynamic properties has been calculated for both models. This includes the chain cross-sectional area, the internal and free energies, the coherence length, the lateral compressibility, and the specific heat. Particular care has been devoted to the transition region, since no analytical results are available in this region for either model. The comparison between the Monte Carlo results for the two models demonstrates that, whereas the two-state model has a first-order transition with jumplike behavior in the transition region the ten-state model exhibits a first-order transition associated with a closed hysteresis loop. Next, the Monte Carlo results for cross-sectional areas per lipid chain, coherence lengths and lateral compressibilities are discussed in the context of experimental results for dipalmitoyl phosphatidylcholine (DPPC). A detailed comparison is made with the results of molecular field calculations throughout the paper. Finally, a Monte Carlo analysis of bilayers composed of both DPPC and cholesterol shows that a two-state model does not adequately describe the thermodynamic behavior of lipid-cholesterol mixtures implying that intermediate states have to be introduced to account for the experimental data.