Two-dimensional ionic liquids with single site anion and cation-neutral dimer are studied by computer simulations and integral equation techniques , with the aim of characterizing differences with single site anion-cation mixtures, and also with three dimensional equivalents of both models , in order to see the competition between the Coulomb interactions and the clustering restrictions due to reduced dimension. We find that the addition of the neutral site to the cation suppresses the liquid-gas transition which occurs in the case of the monomeric Coulomb system. Instead, bilayer membrane type ordering is found at low temperatures. The agreement between the energies and the structural correlations predicted by theory and the simulation is excellent until very close to the no-solution region predicted by the theory. These findings suggest various relations between the nature of the clustering at low temperatures, and the inability of the theory to enter this region.