We investigate bi-component magnonic crystals consisting of periodic square lattices of Co nanodiscs embedded in Permalloy thin films. Micromagnetic simulations are used to analyse experimental data obtained with both all-electrical broadband spectroscopy and inelastic light scattering. We find that complementary spin-wave nanochannels form for in-plane fields H applied even along a non-high symmetry direction of bi-component magnonic crystals in contrast to previously reported magnetic antidot lattices. Depending on the excitation frequency, complementary channels might be functionalized for spin-wave signals transmitted in different spatial directions.