In the present article, we introduce a Hamiltonian model that consists of two modes of the field in a perfect cavity to interact with a single two-level atom. The interaction between the fields has been taken into account and considered to be in the parametric amplifier form. The model in one hand can be regarded as a generalization of the Jaynes–Cummings model (JCM), however, in the other hand it can be considered as a generalization of the parametric amplifier model. Under a certain condition the exact solution to the Schrödinger equation is obtained. Employing this solution and for chosen values of different parameters we discuss numerically the atomic occupation probabilities as well as the degree of entanglement through the entropy of the field. The system shows superstructure phenomenon similar to that appeared from the effect of the Kerr-like medium on the Jaynes–Cummings model. The von Neumann entropy and phase distribution for both two-mode correlated and uncorrelated coherent states cases are also considered.