Carbon nanotube transistors combine molecular-scale dimensions with excellent electronic properties, offering unique opportunities for chemical and biological sensing. Here, we form supported lipid bilayers over single-walled carbon nanotube transistors. We first study the physical properties of the nanotube/supported lipid bilayer structure using fluorescence techniques. Whereas lipid molecules can diffuse freely across the nanotube, a membrane-bound protein (tetanus toxin) sees the nanotube as a barrier. Moreover, the size of the barrier depends on the diameter of the nanotube - with larger nanotubes presenting bigger obstacles to diffusion. We then demonstrate detection of protein binding (streptavidin) to the supported lipid bilayer using the nanotube transistor as a charge sensor. This system can be used as a platform to examine the interactions of single molecules with carbon nanotubes and has many potential applications for the study of molecular recognition and other biological processes occurring at cell membranes.