We investigate the basic features of wave propagation in bianisotropic metamaterials characterized by asymmetric magnetoelectric tensors with zero diagonal elements. The wave propagation is described by a biquadratic dispersion relation with two elliptically polarized eigenwaves. In particular, the bianisotropic media may possess a hybrid character of the elliptic and hyperbolic dispersions. For a wave incident from vacuum onto a bianisotropic medium, there exist an ordinary and an inversion critical angle, leading to angular selective transmission. A standard and a complementary type of angular selective transmissions are illustrated with the incidence of Gaussian beams based on Fourier integral formulation.