Microstructure, phase transitions, electrical conductivity, and optical and electrooptical properties of multiwalled carbon nanotubes (NTs), dispersed in the cholesteric liquid crystal (cholesteryl oleyl carbonate, COC), nematic 5CB and their mixtures, were studied in the temperature range between 255 K and 363 K. The relative concentration X=СОС/(СОС+5CB) was varied within 0.0-1.0. The concentration C of NTs was varied within 0.01-5% wt. The value of X affected agglomeration and stability of NTs inside СОС+5CB. High-quality dispersion, exfoliation, and stabilization of the NTs were observed in COC solvent (“good” solvent). From the other side, the aggregation of NTs was very pronounced in nematic 5CB solvent (“bad” solvent). The dispersing quality of solvent influenced the percolation concentration Cp, corresponding to transition between the low conductive and high conductive states: e.g., percolation was observed at Cp≈1% and Cp≈0.1% for pure COC and 5CB, respectively. The effects of thermal pre-history on the heating-cooling hysteretic behavior of electrical conductivity were studied. The mechanism of dispersion of NTs in COC+5CB mixtures is discussed. Utilization of the mixtures of “good” and “bad” solvents allowed fine regulation of the dispersion, stability and electrical conductivity of LC+NTs composites. The mixtures of COC and 5CB were found to be promising for application as functional media with controllable useful chiral and electrophysical properties.