The subband levels of quantum wells grown in a periodic array form minibands whose bandwidth ⌬ depends on the probability of interlayer tunneling. In the presence of a strong magnetic field, this system of minibands can exhibit various Coulomb-interaction-driven spin polarization instabilities at an integral value of the filling factor ␯. We investigate in particular the Hartree-Fock phase diagram in the case in which the nϭ0 spin-up and nϭ1 spin-down Landau levels are separated by an energy smaller than ⌬. A spin-density-wave ground state is shown to occur at filling factor ␯ϭ2.