The aim of this paper is to explore the possibilities of a novel molecular integral equation approach to produce information on the atom-atom microscopic structure of molecular fluids via multidimensional integration of the molecular pair distribution function. In particular, atom-atom structure factors for hydrogen halides (HCl and HI) are computed from the integral equation for heteronuclear fluids modeled by a two-center Lennard-Jones potential with and without multipole terms. Theoretical results are compared both with experimental partial structure factors and computer simulation results. Theory and simulation agree remarkably well both for thermodynamics and microscopic structure. The comparison with experimental partial structure factors is satisfactory within the limitations due to the rough modeling used for describing the real fluid.