  We study a two-dimensional atomic mixture of bosons and fermions cooled into
their quantum degenerate states and subject to an optical lattice. The optical
lattice provides van Hove singularities in the fermionic density of states. We
find that these van Hove singularities produce new and interesting features for
the transition towards phase separation: an arbitrary weak interaction between
the bosons and the fermions is sufficient to drive the phase separation at low
temperatures. The phase separated state turns stable for attractive and
repulsive interaction between the bosons and fermions and can be cast into the
standard form of a `liquid--gas' transition.
