Recent experiments indicate that the spin-density waves (SDWs) in sTMTTFd2Br, sTMTSFd2PF6, and a-sBEDT-TTFd2MHgsSCNd4 are highly unconventional and coexist with charge-density waves (CDWs). We present a microscopic theory of this unusual CDW-SDW coexistence. A complete understanding requires the explicit inclusion of strong Coulomb interactions, lattice discreteness, the anisotropic two-dimensi...