  This paper characterizes the annealed complexity of bipartite spherical spin
glasses, both pure and mixed. This means we give exact variational formulas for
the asymptotics of the expected numbers of critical points and of local minima.
This problem was initially considered by [Auffinger, Chen 2014], who gave upper
and lower bounds on this complexity. We find two surprising connections between
pure bipartite and pure single-species spin glasses, which were studied by
[Auffinger, Ben Arous, \v{C}ern\'y 2013]. First, the local minima of any pure
bipartite model lie primarily in a low-energy band, similar to the
single-species case. Second, for a more restricted set of pure $(p, q)$
bipartite models, the complexity matches exactly that of a pure $p + q$
single-species model.
