We use two molecular integral equation approximations to compute the thermodynamic properties and microscopic structure of two liquids composed of planar molecules with C-2v symmetry, namely SO2 and H2S. These approximations couple the exact molecular Ornstein-Zernike equation with the hypernetted chain (HNC) and reference-hypernetted chain (RHNC) closures. The theoretical results obtained for various thermodynamic states agree remarkably well with molecular dynamics calculations. In particular, the atom-atom distribution functions are very well reproduced. We find that the RHNC approximation with a hard-sphere fluid reference system offers notable improvement over HNC in the pressure calculation. We include also a self-consistent mean field calculation to incorporate the effect of polarizability on the dielectric constant of liquid SO2. Final results for this quantity are in excellent agreement with experimental values. In contrast, the model used for the electrostatic interactions in H2S leads to anomalously high permanent dipole moments, compared to experiment, and consequently to dielectric constants that an completely off the experimental data. (C) 1997 American Institute of Physics.