Growing carbon nanotubes (CNTs) on the surface of fibers has the potential to modify fiber-matrix interfacial adhesion, enhance composite delamination resistance, and possibly improve toughness. In the present study, aligned CNTs were grown upon carbon fabric via chemical vapor deposition. Continuously monitored single-fiber composite fragmentation tests were performed on pristine and CNT-grafted fibers embedded in epoxy, and single-laminate compact-tension specimens were tested for fracture behavior. A significant increase (up to 20 %) was observed in the interfacial adhesion, at the cost of a decrease in the fiber tensile strength. As a result, the maximum load of the composite was decreased, but its residual load-bearing capacity more than doubled. The likely sources of these effects are discussed, as well as their implications.