The main goal of this paper was to study the dielectric properties of hybrid binary and ternary composites based on biodegradable polymer Ecoflex®, single walled carbon nanotubes (SWCN), and liquid crystalline 4′-pentyl-4-biphenylcarbonitrile (5CB) compound. The obtained results were compared with other created analogically to Ecoflex®, hybrid layers based on biodegradable polymers such as L,D-polylactide (L,D-PLA) and polycaprolactone (PCL). Frequency domain dielectric spectroscopy (FDDS) results were analyzed taking into consideration the amount of SWCN, frequency, and temperature. For pure Ecoflex®, two relaxation processes (α and β) were identified. It was shown that the SWCN admixture (in the weight ratio 10:0.01) did not change the properties of the Ecoflex® layer, while in the case of PCL and L,D-PLA, the layers became conductive. The dielectric constant increased with an increase in the content of SWCN in the Ecoflex® matrix and the conductive behavior was not visible, even for the greatest concentration (10:0.06 weight ratio). In the case of the Ecoflex® polymer matrix, the conduction relaxation process at a frequency ca. several kilohertz appeared and became stronger with an increase in the SWCN admixture in the matrix. Addition of oleic acid to the polymer matrix had a smaller effect on the increase in the dielectric response than the addition of liquid crystal 5CB. Fourier transform infrared (FTIR) results revealed that the molecular structure and chemical character of the Ecoflex® and PCL matrixes remained unchanged upon the addition of SWCN or 5CB in a weight ratio of 10:0.01 and 10:1, respectively, while molecular interactions appeared between L,D-PLA and 5CB. Moreover, adding oleic acid to pure Ecoflex® as well as the binary and ternary hybrid layers with SWCN and/or 5CB in a weight ratio of Ecoflex®:oleic acid equal to 10:0.3 did not have an influence on the chemical bonding of these materials.