Motivated by recent studies of cavity magnon polariton (CMP), we extended a previous theoretical work to generalize microwave transmission calculation with various magnetization boundary condition of YIG thin film embedded in cavity. It is found that numerical implementation given in this paper can be easily applied to other magnetization boundary condition and extended to magnetic multilayers. Numerical results show that ferromagnetic resonance mode of microwave transmission spectrum, which is absent in previous calculation, can be recovered by altering the pinning condition of surface spins. The demonstrated reliability of our theory opens attractive perspectives for studying CMP of thin film with complicated surface magnetization distribution and magnetic multilayers.