Lightning strikes pose a serious natural threat to carbon fiber-reinforced polymers (CFRPs). Knowledge of the electrical current distribution is essential for modeling the interaction between CFRP with lightning. In most applications, the anisotropy of CFRP makes the electrical current tend to concentrate on the surface, having significant influence on the current distribution. The conductivity through the thickness direction was studied with pulse generators and a dedicated four-probe fixture. Nonlinear effects were observed not only for 6.4/69 μs lightning pulses, but also for 20/500 ns pulses with much less energy, in all the three tested composites. The electrical breakdown is a fast process, with voltage spikes observed in the leading edge for a few nanoseconds. After the spikes, the transient resistance remains approximately constant. Similarities could be found with the phenomena involved in thin polymer film breakdowns.