We investigate a candidate structure for the bottom-up design of nanocomposite materials. At a pair of crossing carbon nanotubes, surfactants self-assemble into a micelle-like aggregate incorporating the two tubes. The aggregate forms as long as the gap between the tubes is smaller than the core diameter of a bulk micelle. Moreover, the absorbed surfactant aggregate generates an effective force between the tubes. The dependence of this force oil the distance between the tubes is complex and includes structural components, such as layering. and a large attractive region at larger distances. This attraction appears to be entropic in nature and to originate from confinement of the surfactant head groups.