Topological interface states in one-dimensional electronic and photonic systems are currently intensively investigated. We demonstrate the coupling of topologically confined states: By concatenation of three substructures, where the outer embedding structures have opposite signs of reflection phases to the embedded structure, we realize a system of coupled interface states showing mode splitting. We theoretically and experimentally show that a topological transition occurs for this coupled system. The demonstration of these systems is put on a solid foundation by first realizing the substructures relevant for interface states between topologically distinct one-dimensional photonic crystals. We experimentally demonstrate band closing and band inversion for a redistribution of the optical path to the constitutive materials of the structures. The band inversion is demonstrated by the emergence of interface states at metal-dielectric interfaces and the findings are supported by ellipsometric measurements.