We investigate optical transmission in cavity magnon polaritons and discover a complex multi-window magnetically induced transparency and a bistability with magnetic and optical characteristics. With the regulation of Kerr nonlinear effects and driven fields, a complex multi-window resonant transmission with fast and slow light effects appears, which includes transparency and absorption windows. The magnetically induced transparency and absorption can be explained by the destructive and constructive interference between different excitation pathways. Moreover, we demonstrate the bistability of magnons and photons with a hysteresis loop, where magnetic and optical bistabilities can induce and control each other. Our results pave a new way, to the best of our knowledge, for implementing a room-temperature multiband quantum memory.