Seven cosmological hydrodynamic simulations of disk galaxy formation are analyzed to determine the alignment of the disk within the dark matter halo and the internal structure of the halo. We find that the orientation of the outer halo, beyond ~0.1 r_vir, is unaffected by the presence of the disk. In contrast, the inner halo is aligned such that the halo minor axis aligns with the disk axis. The relative orientation of these two regions of the halo are uncorrelated. The alignment of the disk and inner halo appears to take place simultaneously through their joint evolution. The disconnect between these two regions of the halo should be taken into account when modelling tidal streams in the halos of disk galaxies and when calculating intrinsic alignments of disk galaxies based on the properties of dark matter halos. ; Comment: To be published in ApJL, 5 pages, 3 figures