A challenging problem in the biophysics of cell membranes is the characterization of the lateral organization of their domains. These domains are made up of lipids in an ordered phase and are dispersed in a more disordered continuous lipid phase. A widely used experimental model to study these systems are the lipid monolayers at the water-air interface. Based on these experiments and using Brownian simulations, we study how the dipolar interaction between domains affects the structure of monolayers with phase coexistence. We present a new way to estimate the dipole repulsion directly from the experimental results. Besides, we also study an analytical approach to this system based on the Ornstein-Zernike integral equation theories (OZ-IETs). When the pair correlation function serves as the measure, we found that the closures that outperform better are the Modified Hypernetted Chain (MHNC) and the Variational Modified Hypernetted Chain (VMHNC), with a reference system based on an extension of the hard spheres parametrization. On the other hand, when the structure factor is used as a measure, the reference system that performs better depends on the particular region of the phase diagram.