The possible contribution of fullerenes and their derivatives to the diffuse interstellar bands (DIBs) has been discussed for some time. Bare fullerenes have been identified in the interstellar medium but they explain few, if any, of the DIBs. In this contribution we show that C+ 60 and C+ 70 will physisorb copious amounts of molecular hydrogen at low temperature. H2 forms an ordered layer around the fullerene ion; the first coordination shell closes when each carbon ring is decorated with one H2. We estimate that fullerenes in dense clouds may very well be complexed with H2. The occurrence of H2-fullerene complexes in translucent clouds is less likely but cannot be ruled out. They are unlikely to occur in diffuse clouds, which are the major sources of DIBs.