We discuss a simple first-principles homogenization theory for describing, in the long-wavelength limit, the effective bianisotropic response of a periodic metamaterial composite without intrinsic chiral and magnetic inclusions. In the case where the dielectric contrast is low, we obtain a full analytical description which can be considered the extension of Landau-Lifshitz-Looyenga effective-medium formulation in the context of periodic metamaterials.