Phase diagrams of mixtures of an acrylate-based nematic side-chain polymer and chiral nematics, which form blue phases, were deduced from polarized light microscopy. The blue phase can he used as a probe of miscibility since it is sensitive to small amounts of impurities. Miscibility appears to be enhanced by the flexibility of the parent compounds and dipole-dipole interaction: it is characterized by decreased transition temperatures and stabilized phases.