  We consider a rapidly rotating two-component Bose-Einstein condensate with
short-range s-wave interactions as well as dipolar coupling. We calculate the
phase diagram of vortex lattice structures as a function of the intercomponent
s-wave interaction and the strength of the dipolar interaction. We find that
the long-range interactions cause new vortex lattice structures to be stable
and lead to a richer phase diagram. Our results reduce to the previously found
lattice structures for short-range interactions and single-component dipolar
gases in the corresponding limits.
