We derive and discuss an experimentally realistic model describing ultracold atoms in an optical lattice including a commensurate, but staggered, spin-flip term. The resulting band structure is quite exotic; fermions in the third band have an unusual rounded picture-frame Fermi surface (essentially two concentric squircles), leading to imperfect nesting. We develop a generalized theory describing the spin and charge degrees of freedom simultaneously at the random-field-approximation level, and show that the system can develop a coupled spin-charge-density wave order. Our generic approach can be used to study spin and charge instabilities in many materials, such as high-T-c superconductors, organic compounds, graphene, and iron pnictides. Copyright (C) EPLA, 2012