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Formation of the inventive polymer composite matrix begins by growing carbon nanotubes directly on a veil substrate. The carbon nanotubes are grown from both sides of a non woven carbon fiber mat. The carbon nanotubes can be single or multi walled and can be grown to predetermined lengths. The veiled substrate is positioned between carbon fiber/ polymer prepreg layers such that the carbon nanotubes protrude into the reinforcement layers. The polymer composite matrix formed following curing of the resin exhibits improved interlaminar strength, fracture toughness and impact resistance. Because of the thinness of the veil layer, electricity can pass from conductive carbon nanotubes on one side of the veil to conductive carbon nanotubes on the other side of the veil. Electricity can also pass between two veils intercalated into the same reinforcement layer when the length of the nanotubes is sufficiently long enough to provide overlap within the reinforcement layers.