The generalized exponential matrix technique in the spectral domain is used in conjunction with Galerkin's approach to examine the dispersion characteristics of bilateral coplanar waveguide and periodic microstrip line in bianisotropic superstrate-substrate structures possessing different constitutive features, and the mathematical treatment in this study accounts for very generalized bianisotropic linear media characterized by four independent 3 x 3 constitutive tensors but within the confines of a realizable physical range. Numerical results are presented to demonstrate the combined effects of magnetoelectric cross coupling on the propagation constant of dominant mode, and some unique dispersion phenomena are illustrated and discussed.