The shear behavior and the normal interaction between mica surfaces covered by surfactant or surfactant-polymer mixtures were studied with a Surface Forces Apparatus (SFA) nanotribometer. If the surfaces are compressed while fully immersed in an aqueous surfactant solution that adsorbs in the form of flat bilayers, hemifusion can be induced. When the hemifused surfaces are subject to shear, at least five different dynamic regimes can be recognized. The general behavior may be described by a model based on the kinetics of formation and rupture of adhesive bonds between the shearing surfaces, with an additional viscous term. Once the adsorbed surfactant layer is decorated with physigrafted copolymers, the number of sliding regimes may be reduced to only one, in which the shear stress increases sublinearly with the driving velocity. The adhesion energy and the resistance to hemifusion of the adsorbed surfactant-polymer layers are also strongly modified as the grafting density increases.