  We show that the interplay of a high density two-dimensional electron gas and
localized electrons in a neighboring Mott insulator leads to kinetic magnetism
unique to the Mott/band insulator interface. Our study is based upon a bilayer
Hubbard model at $U=\infty$ with a potential difference between the two layers.
We combine analytic results with DMRG simulations to show that magnetism, and
especially ferromagnetism, is greatly enhanced relative by the proximity of the
two subsystems. The results are potentially relevant to recent experiments
suggesting magnetism in $R$TiO$_3$/SrTiO$_3$ heterostructures.
