The authors introduce a coarse-grained (CG) model for a lipid membrane comprised of phospholipids and cholesterol at different molar concentrations, which allows them to study systems that are approximately 100nm in linear size. The systems are studied in the fluid phase above the main transition temperature. The effective interactions for the CG model are extracted from atomic-scale molecular dynamics simulations using the inverse Monte Carlo (IMC) technique, an approach similar to the one the authors used earlier to construct another CG bilayer model [T. Murtola et al., J. Chem. Phys.121, 9156 (2004)]. Here, the authors improve their original CG model by employing a more accurate description of the molecular structure for the phospholipid molecules. Further, they include a thermodynamic constraint in the IMC procedure to yield area compressibilities in line with experimental data. The more realistic description of the molecular structure of phospholipids and a more accurate representation of the interaction between cholesterols and phospholipid tails are shown to improve the behavior of the model significantly. In particular, the new model predicts the formation of denser transient regions in a pure phospholipid system, a finding that the authors have verified through large scale atomistic simulations. They also find that the model predicts the formation of cholesterol-rich and cholesterol-poor domains at intermediate cholesterol concentrations, in agreement with the original model and the experimental phase diagram. However, the domains observed here are much more distinct compared to the previous model. Finally, the authors also explore the limitations of the model, discussing its advantages and disadvantages.