Miscibility phase diagrams of mixtures of side-on side chain liquid crystalline polymers (s-SCLCP) and low molar mass liquid crystals (E48 and E44) have been established by means of polarized optical microscopy and light scattering. E48 and E44 are cyanobiphenyl-based eutectic nematic liquid crystal (LC) mixtures with nematic-isotropic transition temperatures of 93 and 105 C, respectively. The phase diagram of the s-SCLCP/E48 system reveals the coexistence of an isotropic nematic region and a single nematic phase in order of descending temperature. The single nematic phase suggests that the pair is miscible in the nematic region. On the other hand, the s-SCLCP/E44 mixture shows liquid liquid and nematic nematic coexistence phases, suggestive of the immiscibility character of the pair. These nematic phase diagrams of the s-SCLCP/E48 and s-SCLCP/E44 have been analysed in the context of the combined Flory-Huggins (FH) free energy for isotropic mixing and the Maier-Saupe (MS) free energy for nematic ordering of the mesogens. This combined FH/MS theory is capable of predicting the observed nematic phase diagrams consisting of liquid liquid, liquid nematic, nematic nematic, and the pure nematic regions. The change of colour accompanying the appearance and disappearance of the inversion walls may be attributed to the temperature dependence of birefringence.