Due to their mechanical robustness and chemical resistance, composite electrospun membranes based on polyvinyl chloride (PVC) are suitable for sensor applications. Aiming to improve the electrical characteristics of these membranes, this work investigated the effects of the addition of carbon nanotubes (CNTs) to PVC electrospun membranes, in terms of morphology and thermal and impedance behavior. Transmission electron microscopy images evidenced that most of the nanotubes were encapsulated within the fibers and oriented along them, while field-emission scanning electron micrographs revealed that the membranes consisted of uniform fibers with an average diameter of 339 ± 31 nm, regardless of the addition of the carbon nanotubes. With respect to the neat resin, the addition of nanotubes caused a significant lowering of the glass transition temperature (up to 20 °C) and a marked change in the second degradation step of PVC. Nyquist plots from electrical impedance spectra showed a charge transfer resistance (RCT) of 38 and 40 MΩ for neat PVC and PVC/CNT 3 wt.% membranes, respectively, indicating that, in the dry state, the encapsulation of CNTs in the fibers and the high porosity of the membranes prevented the formation of a percolation network, increasing the electrical resistance. In the wet state, however, there was a greater change in the impedance behavior, decreasing the resistance RCT to 4.5 and 1.1 MΩ, for neat PVC and PVC/CNT 3 wt.% membranes, respectively. The results of this study, showing a significant variation in impedance behavior between dry and wet membranes, are relevant for the development of various types of sensors based on PVC composites.