A one-dimensional multilayer structure consisting of two symmetric parts with defect layers is designed, and properties of the multiple nonreciprocal transmission are investigated due to symmetrically distributed magneto-optic layers with opposite magnetic fields in composite structures. The transmission coefficient and energy band diagram of the system are obtained based on transfer matrix method. The numerical results show that there are three pairs of nonreciprocal dispersive curves with different modes in a certain bandgap. The influence of the thickness of defect layer and incident angle on nonreciprocal frequencies is also discussed. The multiple nonreciprocal transmission could in turn be potentially useful in optical isolators and optical resonators.