Using a coarse-grained lipid and peptide model, we show that the free energy stabilization of amyloid-β in heterogeneous lipid membranes is predicted to have a dependence on asymmetric distributions of cholesterol compositions across the membrane leaflets. We find that a highly asymmetric cholesterol distribution that is depleted on the exofacial leaflet but enhanced on the cytofacial leaflet of the model lipid membrane thermodynamically favors membrane retention of a fully embedded Aβ peptide. However, in the case of cholesterol redistribution that increases concentration of cholesterol on the exofacial layer, typical of aging or Alzheimer's disease, the free energy favors peptide extrusion of the highly reactive N-terminus into the extracellular space that may be vulnerable to aggregation, oligomerization, or deleterious oxidative reactivity.