Molecular interaction energy is studied in terms of the double symmetry-adapted perturbation theory, taking account of both the electronic exchange between molecules and the intracorrelation fluctuation for individual monomers. The energy is divided into physically meaningful components, such as electrostatic, first-order exchange, second-order polarization, and second-order exchange terms. The algebraic expressions of second-order component energy terms, especially second-order exchange ones, are derived for the interaction of two-electron systems by considering only single-electronic exchanges between molecules. Our result for the He dimer is compared with that produced when the explicitly correlated Gaussian-type geminal is employed. The ratio of intracorrelation energy to Hartree-Fock energy in the second-order exchange is larger than those in the second-order polarization as well as in the first-order energies. The interaction energies of the H-2 dimer including intracorrelation effect are computed in four orientations, i.e., linear, parallel, T, and X types.