Epitaxial Bi2FeMnO6 (BFMO) thin films deposited on various Nb:SrTiO3 substrates show that the lattice parameters are very sensitive to epitaxial strains. Compressive and tensile strains are induced to the in-plane lattice constants of the (100) and (111) oriented films, respectively, while that of the (110) oriented thin film stay unstrained. The thin films also exhibit a strongly anisotropic growth habit depending on the substrate. Spiral growth, such as in the (100) BFMO film, is unique in samples prepared by pulsed laser deposition. Extrinsic dielectric constants at low frequencies are attributed to oxygen vacancies via the Maxwell-Wagner effect. All the samples show saturated hysteresis loops with very small coercive fields at 200 K, indicating the presence of weak ferromagnetism.