No instrument is able to measure directly the quantum entanglement of a system. However, both theory and experiment, following the well-known Bell inequality, reveal the existence of the entanglement phenomenon in quantum mechanics. To examine the characterization of quantum entanglement, here we present a two-site cavity system, in which each cavity contains a Λ-type three-level atom and the two sites are identical and coupled with each other. We investigate and calculate the bipartite entanglement entropy of the system for the ground states. For photons of different types, corresponding to the two ground states of the atom, we investigate the correlations and violation of the Bell inequality.