  We generalize the typical medium dynamical cluster approximation to multiband
disordered systems. Using our extended formalism, we perform a systematic study
of the non-local correlation effects induced by disorder on the density of
states and the mobility edge of the three-dimensional two-band Anderson model.
We include inter-band and intra-band hopping and an intra-band disorder
potential. Our results are consistent with the ones obtained by the transfer
matrix and the kernel polynomial methods. We apply the method to
K$_x$Fe$_{2-y}$Se$_2$ with Fe vacancies. Despite the strong vacancy disorder
and anisotropy, we find the material is not an Anderson insulator. Our results
demonstrate the application of the typical medium dynamical cluster
approximation method to study Anderson localization in real materials.
