The eigenproblems of quantized spin waves in a (100) ferromagnetic bilayer system have been investigated theoretically by using the interface rescaling approach. The energy-band structure of the system has been obtained and the effect of the uniaxial bulk anisotropy field of easy-axis type on the energy bands were explored thoroughly. It is found that there are bulk modes, perfect confined modes and interface modes in the biferromagnetic system, the existing condition of which is determined not only by the bulk exchange coupling constant, the interface exchange coupling constant, the spin of lattice, the number of atomic layers, but also by the uniaxial bulk anisotropy.