Using replica exchange with solute tempering all-atom molecular dynamics, we studied the equilibrium binding of Aβ25-35 peptide to the ternary bilayer composed of an equimolar mixture of dimyristoylphosphatidylcholine (DMPC), N-palmitoylsphingomyelin (PSM), and cholesterol. Binding of the same peptide to the pure DMPC bilayer served as a control. Due to significant C-terminal hydrophobic moment, binding to the ternary and DMPC bilayers promotes helical structure in the peptide. For both bilayers a polarized binding profile is observed, in which the N-terminus anchors to the bilayer surface, whereas the C-terminus alternates between unbound and inserted states. Both ternary and DMPC bilayers feature two Aβ25-35 bound states, surface bound, S, and inserted, I, separated by modest free energy barriers. Experimental data are in agreement with our results but indicate that cholesterol impact is Aβ fragment dependent. For Aβ25-35, we predict that its binding mechanism is independent of the inclusion of PSM and cholesterol into the bilayer.