Input-output analysis of transitional channel flows has proven to be a valuable analytical tool for identifying important flow structures and energetic motions. The traditional approach abstracts the nonlinear terms as forcing that is unstructured, in the sense that is not directly tied to the underlying nonlinearity in the dynamics. This paper instead employs a structured singular value-based approach that preserves certain input-output properties of the nonlinear forcing function in an effort to recover the larger range of key flow features identified through nonlinear analysis, experiments, and direct numerical simulation (DNS) of transitional channel flows. Application of this method to transitional plane Couette and plane Poiseuille flows leads to identification of not only the streamwise coherent structures predicted through traditional input-output approaches but also characterization of the oblique flow structures as those requiring the least energy to induce transition in agreement with DNS studies, and nonlinear optimal perturbation analysis. The proposed approach also captures the recently observed oblique turbulent bands that have been linked to transition in experiments and DNS with very large channel size. The ability to identify the larger amplification of the streamwise varying structures predicted from DNS and nonlinear analysis in both flow regimes suggests that the structured approach allows one to maintain the nonlinear effects associated with the saturation of the lift-up mechanism, which is known to dominate the linear operator. Capturing this key nonlinear mechanism enables the prediction of the wider range of known transitional flow structures within the analytical input--output modeling paradigm.