Polymer-matrix composites containing conductive nanoparticles are a potential means for achieving an appealing combination of multifunctional properties for their use as structural parts in the aerospace field. Carbon nanofibers (CNFs) have been being looked forward to as the next generation of new and avant-garde aircraft structures because they are exceptionally coveted competitor materials to replace traditional metal components for lightning strike protection. In this regard, nanocomposites at low concentration of CNFs ranging from 0.05% up to 2% by wt to impart electron conduction in tetrafunctional epoxy resin have been prepared and characterized. The aim of this work concerns the use of Tunneling AFM (TUNA) as revolutionary tool able to correlate the electrical current map with the correspondent local morphology of CNF/resins. TUNA technique has proven to play a leading role in the identification of current paths and electrical interconnections, even without altering the morphology with usual treatments employed to create electrical contacts to the ground. Summing up, the good electrical performance together with the high mechanical properties due to a conductive cross-linked network of CNFs inside the resin demonstrate a charming applicative potential for the formulated nanocomposites as structural materials capable to provide a safe conductive path on the exterior skin, preventing serious damage to the aircraft.