The influence of branched poly(ethyleneimine) on the phase behavior of the system sodium dodecylsulfate/toluene-pentanol (1:1)/water has been studied. The isotropic microemulsions still exist when water is replaced with aqueous solutions of PEI (up to 30% in weight), but their stability is significantly influenced. From a polymer concentration of 20 wt%, the polymer enhances the solubilization of water in oil, changes the sign of the spontaneous curvature of the surfactant film, and induces an inversion of the microemulsion type from water-in-oil (L(2)) to oil-in-water (L(1)), by the formation of a bicontinuous channel. Further investigations show that the addition of polymer in the L(2) phase changes the droplet-droplet interactions as the conductivity drops and the percolation disappears. In the bicontinuous channel, higher viscosities can be detected, as well as a weak percolation followed by a steep increase of the conductivity, which can be related to evident structural changes in the system. DSC measurements allow then to follow the changes of the water properties in the system, from interfacial-water in the L(2) phase to free-water in the sponge-like phase. Finally, all the measurements performed permit to characterize the structural transitions in the system and to understand the role of the added polymer.