We study the magnetic phase diagram of a superlattice fabricated from ferromagnetic films, with interfilm exchange coupling provided by intervening nonferromagnetic layers. We suppose the interfilm exchange coupling contains a biquadratic component, with magnitude comparable to the linear exchange, as found recently in the Fe/Cr(211) structures. Our analysis centers on these materials, where the Fe magnetizations lie in plane, which also contains a twofold anisotropy axis. Sufficiently large biquadratic exchange produces important qualitative modifications of the magnetization curves, and can introduce new magnetic phases. We illustrate with results for infinite superlattices, and for finite superlattices with either an even or odd number of ferromagnetic layers.