An inverse problem for a stratified slab of a general bianisotropic medium is considered in the frequency domain. Considering obliquely impinging plane waves, imbedding equations and Green's functions equations for the reflection and transmission coefficient matrices and the internal fields are derived through the concept of wave-splitting. Two different optimization approaches, based on the imbedding method and the Green's functions method respectively, are applied to reconstruct the constitutive parameters as functions of the position using band-limited reflection and/or transmission data from different angles of illumination. Exact and explicit expressions for the gradients are derived, which result in a one order faster computation compared with numerical perturbations of the objective functionals. The reconstruction algorithm (based upon a conjugate gradient method) is tested with both clean and noisy data.