The influence of nanometer thick, highly anisotropic organically modified layered silicate (montmorillonite) on the phase behavior of deuterated polystyrene (dPS) and poly(vinyl methyl ether) (PVME) is investigated by a combination of small-angle neutron scattering (SANS) and a two-dimensional combinatorial method based on light scattering and corroborated by single-point static cloud-point light scattering. The presence of layered silicates up to a volume fraction of 0.04 is found to leave the phase diagram essentially unchanged, with the values of the Flory-Huggins chi parameter at high temperatures being nearly independent of added silicate for blends with layered silicates up to a volume fraction of 0.008. These surprising results, in light of the significantly higher polarity of PVME in comparison to PS, allows us to investigate the influence of such layered silicates on the kinetics and morphology of phase separation in polymer blends as detailed in a previous paper.