Drug-membrane interactions are well known but poorly understood. Here we describe dual measurements of membrane thickness change and membrane area change due to the binding of the amphipathic drug curcumin. The combined results allowed us to analyze the binding states of a drug to lipid bilayers, one on the water-membrane interface and another in the hydrocarbon region of the bilayer. The transition between the two states is strongly affected by the elastic energy of membrane thinning (or, equivalently, area stretching) caused by interfacial binding. The data are well described by a two-state model including this elastic energy. The binding of curcumin follows a common pattern of amphipathic peptides binding to membranes, suggesting that the binding states of curcumin are typical for amphipathic drugs.