Complex fluids containing crystallizing fatty acids are important for consumer care products. The key features of these materials are their ability to support their weight under gravity due to the formation of a fatty acid crystal network, and to yield or flow beyond a critical applied strain. In model formulations comprised of two synthetic surfactants and a fatty acid in water, we have shown that the fatty acid crystal network consists of crystal aggregates linked by a non-crystallized mixed fatty acidsurfactant mesophase. We hypothesize that this mixed surfactant-fatty acid mesophase is critical for the macroscopic stability of the formulations. Rheological measurements combined with differential scanning calorimetry (DSC), X-ray scattering, and polarized light microscopy (PLM) measurements show the importance of surfactant loading on the overall stability of the formulations by linking morphology to rheology. Macroscopically homogeneous formulations are realized with 7-10 wt% of fatty acid. Increasing the fatty acid content without adding surfactant leads to inhomogeneous, phase separating formulations. Although both stable and unstable formulations show the presence of a surfactant-fatty acid mixed phase, a critical loading of surfactants is found to be necessary to create macroscopically homogenous formulations. We demonstrate how the rheology, microstructure and the macroscopic stability can be tuned by varying the relative amounts of surfactants and fatty acid.