We explore the phase behavior of lipid bilayers containing SOPC (1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine) with various molar concentrations (0 mol%, 10 mol% and 30 mol%) of cholesterol. To this end, we performed extensive atomistic molecular dynamics simulations in conjunction with the Slipids force field with optimized parameters for the headgroups of phospholipids. We computed thermodynamic and structural quantities describing the ordering of the tails, the mobility of the heads and the arrangement of the lipids in the bilayers. We analyzed the behavior of the named quantities over the temperature range between 271 K and 283 K, where the experimentally determined melting temperature, Tm=279 K, lies, as well as at 400 K, which is used as a reference temperature. The obtained results are compared to available experimental data along with the outcome from molecular dynamics simulations of similar phospholipids containing different amounts of cholesterol. In the temperature interval of interest, we found evidence of the occurrence of a thermal-driven phase transition (melting) in both the pure system and the one with the lower concentration of cholesterol, while in the remaining system, the higher amount of cholesterol in the bilayer smears out the transitional behavior. Thus, we demonstrate the ability of the Slipids force field to predict the phase behavior of bilayers of SOPC and SOPC mixed with cholesterol.