A small-angle light-scattering (SALS) technique is performed to investigate the phase separation in the films of flexible polymer (polystyrene, PS) mixed with low molecular weight thermotropic liquid crystal LC (4-cyano-4'-n-octylbiphenyl, 8CB). The growth of isotropic (polymer) domains is studied in both isotropic and anisotropic (nematic or smectic phase) LC matrices, as a function of time, film thickness, and film composition. The size of the domains, L(t), grows algebraically with time as L(t) similar to t(beta). For 70/30 wt % of 8CB/PS, we found the diffusion growth in isotropic (beta = 0.25) and smectic (beta = 0.28) matrices, independent of the film thickness. In the nematic matrix, beta changes from 0.33 to 0.47 as we change the thickness of the sample from 120 to 10 mum. We think that the change of beta is due to the attractive forces between the polymer domains which follow from the elastic deformations of the nematic matrix caused by the glass surfaces and polymer domains. In every matrix and for different thicknesses of a sample, scaling is observed in this growth regime. At longer times, there is a crossover from the diffusion growth to the hydrodynamic fast-mode growth, characteristic for systems in which one of the components wets the confining walls. In this regime, we do not observe the scaling; i.e., there is more than one characteristic length scale in the system, and beta ranges from 1 to 3/2. Considering extremely viscous systems (50/50 wt % of 8CB/PS), we also find the diffusion growth but with smaller exponent beta < 0.2. In this case, we observe two peaks in the scattering intensity S(q,t). One of them is the surface and one the bulk peak. For systems with small amount of a polymer (90/10 wt % of 8CB/PS), the process of growth is very fast, and beta = 0.4. In this case, the bulk peak is very quickly covered by the peak coming from the growth of the domains at the surface. To perform the measurements in anisotropic LC systems, we had to eliminate the multiple scattering of light coming from the large difference in ordinary and extraordinary refractive indexes of LC.