The surface dilational modulus--or compressibility modulus--has been previously studied for monolayers composed of pure materials, where a jump in this modulus was related with the onset of percolation as a result of the establishment of a connected structure at the molecular level. In this work, we focused on monolayers composed of two components of low lateral miscibility. Our aim was to investigate the compressibility of mixed monolayers at pressures and compositions in the two-phase region of the phase diagram, in order to analyze the effect of the mechanical properties of each phase on the stiffness of the composite. In nine different systems with distinct molecular dipoles and charges, the stiffness of each phase and the texture at the plane of the monolayer were studied. In this way, we were able to analyze the general compressibility of two-phase lipid monolayers, regardless of the properties of their constituent parts. The results are discussed in the light of the following two hypotheses: first, the stiffness of the composite could be dominated by the stiffness of each phase as a weighted sum according to the percentage of each phase area, regardless of the distribution of the phases in the plane of the monolayer. Alternatively, the stiffness of the composite could be dominated by the mechanical properties of the continuous phase. Our results were better explained by this latter proposal, as in all the analyzed mixtures it was found that the mechanical properties of the percolating phase were the determining factors. The value of the compression modulus was closer to the value of the connected phase than to that of the dispersed phase, indicating that the bidimensional composites displayed mechanical properties that were related to the properties of each phases in a rather complex manner.