Using the methods of angular correlation of annihilation radiation, attenuation of electromagnetic radiation in 1.5–2 2 GHz frequency range, and optical ellipsometry, it was shown that a 2% decrease in the probability of annihilation of positrons in pores of free volume leads to changes in the parameters of electronic structure of composites by 15–25% in composites of polytetrafluoroethylene (PTFE) + multiwalled carbon nanotubes (MWCNTs). Polytetrafluoroethylene is transparent to electromagnetic radiation, but after the addition of 10 wt% multiwalled carbon nanotubes, the composite demonstrates a more than 400-fold decrease in the electromagnetic radiation intensity when the radiation passes through a specimen with a thickness of ≈2 mm. It was found that the average radius of the free volume pores and the probability of annihilation of positrons in this area are determined by the electronic structure parameters of the polymer matrix only. The Fermi angle and the probability of positrons annihilation with free electrons are determined by the electronic structure parameters of MWCNTs only. Since the electronic structure of the cores and defects of the polymer matrix (at least outside the interphase) does not change, changes in these characteristics are mainly due to changes in the MWCNTs electronic structure. It was found that in a specimen with 10 wt% MWCNTs, the highest density of free electrons is observed, and the highest electron density is observed on defects. The average of free volume pore radius reaches its maximum value at 10 wt% MWCNTs in the composite.