We develop a free energy model that describes two key thermodynamic properties, the osmotic pressure I and the linear elastic shear modulus G'(p) (i.e. plateau storage modulus), of concentrated monodisperse emulsions which have isotropic, disordered, droplet structures, and are stabilized using ionic surfactants. This model effectively incorporates the concept of random close packing or jamming of repulsive spheres into a free energy F that depends on droplet volume fraction I center dot and shear strain gamma both below and above the a critical jamming point I center dot (c) ae 0.646. This free energy has three terms: entropic, electrostatic, and interfacial (EEI). By minimizing F with respect to an average droplet deformation parameter that links all three terms, we show that the entropic term is dominant for I center dot well below I center dot (c), the electrostatic term is dominant for I center dot near but below I center dot (c), and the interfacial term dominates for larger I center dot. This EEI model describes measurements of G'(p)(I center dot) for charge-stabilized uniform emulsions having a wide range of droplet sizes, ranging from nanoscale to microscale, and it also is consistent with measurements of I (I center dot). Moreover, it describes G'(p)(I center dot) for similar nanoemulsions after adding non-amphiphilic salt, when changes in the interfacial tension and the Debye screening length are properly taken into account. By unifying existing approaches, the EEI model predicts constitutive properties of concentrated ionic emulsions that have disordered, out-of-equilibrium structures through near-equilibrium free energy minimization, consistent with random driving Brownian excitations.