Based on the transfer matrix method, we calculate the impedance of a one-dimensional finite photonic structure to study the existing condition of interface states of layered composite structures with inversion symmetry. For two photonic structures with different inversely symmetric centers, the imaginary parts of their impedance have the opposite sign in all the odd bandgaps and the same sign in the even bandgaps. Therefore, The composite structure composed of the two individual photonic structures exhibits one interface state at the characteristic frequency where the sum of the impedance imaginary parts in the odd bandgaps of the two individual structures is equal to zero, and meanwhile the imaginary part of impedance of the composite structure is also zero at the characteristic frequency. If one composite structure is composed of multiple finite layered structures with different inversely symmetric centers in the way of alternating arrangement, and then in the same odd bandgaps, multiple interface states will appear. The imaginary part of impedance of the composite structure at the characteristic frequency is zero, and the electric field distribution of the interface state optical wave shows significant localization at the composite interface. In addition, the positions of multiple interface states can be adjusted to meet different application requirements by changing the unit cell number of one part of the composite structure.