We use molecular dynamics simulations to characterize the influence of cholesterol (Chol) on the interaction between the anticancer drug doxorubicin (DOX) and a dipalmitoyl phosphatidylcholine/Chol lipid bilayer. We calculate the potential of mean force, which gives us an estimate of the free energy barrier for DOX translocation across the membrane. We find free energy barriers of 23.1 ± 3.1 kBT, 36.8 ± 5.1 kBT, and 54.5 ± 4.7 kBT for systems composed of 0%, 15%, and 30% Chol, respectively. Our predictions agree with Arrhenius activation energies from experiments using phospholipid membranes, including 20 kBT for 0% Chol and 37.2 kBT for 20% Chol. The location of the free energy barrier for translocation across the bilayer is dependent on composition. As Chol concentration increases, this barrier changes from the release of DOX into the water to flip-flop over the membrane center. The drug greatly affects local membrane structure by attracting dipalmitoyl phosphatidylcholine headgroups, curving the membrane, and allowing water penetration. Despite its hydrophobicity, DOX facilitates water transport via its polar groups.