We present evidence that the organic/third phase transition, as may be observed in the Plutonium Uranium Reduction EXtraction process (PUREX) at high metal loading, is an unusual transition between two isotropic, bi-continuous micro-emulsion phases. As this system contains so many components, however, we seek first to investigate the properties of a simpler system, viz. the related metal-free, quaternary system of water/n-dodecane/nitric acid/tri-butyl phosphate (TBP). Under appropriate conditions, this system exhibits three coexisting phases, namely the light organic phase, the third phase and the aqueous phase. In this paper, we focus on the two phase coexistence between the light organic and the third phase. Using Gibbs Ensemble Monte Carlo (GEMC) simulations, we find phase-coexistence between a phase rich in nitric acid and dilute in n-dodecane (the third phase) with a phase more dilute in nitric acid and rich in n-dodecane (the light organic phase). The compositions and densities of these two co-existing phases are in good agreement with experiment. Because the systems are dense and the molecules involved are not simple, the particle exchange rate in the GEMC simulation can be rather low. To show that the system, at a composition intermediate between that of the observed third and organic phases, is indeed unstable with respect to phase separation, we use the Bennett acceptance ratio method to calculate the Gibbs energies of the homogeneous phase and the weighted average of the two co-existing phases, where the compositions of these phases were taken both from GEMC and from experiment. Both demixed states have a statistically significant lower Gibbs energy than the uniform, mixed phase, providing confirmation that GEMC correctly predicts phase separation. Snapshots from the simulations as well as the cluster analysis of the organic and third phases reveal structures akin to bi-continuous micro-emulsion phases, where the polar species reside within a mesh whose surface consists of amphiphilic TBP molecules. The non-polar n-dodecane molecules are outside this mesh. The large-scale structural differences between the two phases lie solely in the dimensions of the mesh. Evidence for the correctness of these structures comes from small-angle X-ray scattering (SAXS), where the profiles obtained for both the organic and third phases agree well with those calculated from simulation. Finally we look at the microscopic structures of the two phases. In the organic phase, the basic motif is that of one nitric acid molecule hydrogen bonded to a TBP. In the third phase, the most common structure was that of the hydrogen bonded chain TBP–HNO3–HNO3. A cluster analysis provides evidence that the TBP forms an extended, connected network in both phases. Studies of the effects of metal ions on these systems will be presented elsewhere, but suffice it to say here that these ions do not change the basic bi-continuous structure of the phases. The metal ions reside inside the mesh along with the other polar molecules.