<p>It is well-known that the rotating wave approximation (RWA) is valid in the weak coupling regimes in atom-field interaction, while counter rotating terms (CRTs) cannot be ignored in the strong coupling regimes. It is also approved that, considering CRTs is equivalent to the presence of a typical nonlinearity function in the atom-field interaction Hamiltonian, which makes it possible to achieve a solution for the dynamical system. With these considerations, in this paper, using the perturbation theory and the nonlinear coherent state approach, we first intend to solve the Hamiltonian interaction between a two-mode field with two qubits (two-level atoms) in a high-quality cavity, while the two-photon atomic transitions are allowed and CRTs are taken into account. We then solve the time-dependent Schrödinger (TDSh) equation with special initial conditions for the considered model, wherein the dipole-dipole interaction (D-DI) is also considered. In the continuation, concurrence (atomic population inversion), as a suitable measure for the amount of entanglement between the two qubits (energy exchange between atoms and field) is evaluated, numerically. At the same time, we examine the effect of CRTs and D-DI (as well as other related parameters involved in the model interaction) on these quantities. Our results show that, CRT and D-DI obviously change the entanglement and atomic population inversion patterns, however, the same maximum values of entanglement and favorable patterns of atomic inversion may still be achieved, depending on the chosen initial atom-field conditions.</p>