Foam drainage varies with the type of surfactant. We present direct measurements of the flow velocity profiles across single Plateau borders using confocal microscopy. For protein foams the interface is rigid, whereas small-surfactant foams show significant interfacial mobility. The results agree with a model that takes into account the shearing of the liquid/gas interface transverse to the flow direction. A significant consequence is that bubble size and liquid volume fraction in a foam affect the relative importance of surface rheology on the drainage behavior.