Neutron reflectometry with in situ rheology is used to measure the shear response of an adsorbed anionic surfactant (sodium bis(2-ethylhexyl) sulfosuccinate, AOT) at the alumina-water interface. A low surfactant concentration is measured where a single bilayer adsorbs at the interface as well as a higher concentration where a multilamellar structure forms. The low concentration structure does not change with the imposed shear (oscillatory or steady). However, the lamellar phase shows a loss of structure under both steady and oscillatory shear. There are differences between the steady and oscillatory cases, which are discussed, with both showing a strong dependence on the strain amplitude.