  A theoretical model is proposed for the (0,0,1) superlattice manganite system
(LaMnO$_3$)$_n$(SrMnO$_3$)$_m$. The model includes the electron-electron,
electron-phonon, and cooperative Jahn-Teller interactions. It is solved using a
version of single-site the dynamical mean field approximation generalized to
incorporate the cooperative Jahn-Teller effect. The phase diagram and
conductivities are calculated. The behavior of the superlattice is found to a
good approximation to be an average over the density-dependent properties of
individual layers, with the density of each layer fixed by electrostatics.
