We report on the microstructural study in a cross section of the ternary phase diagram of pentaethylene glycol mono-n-dodecyl ether (C12E5)/water/random heteropolymer defined by the surfactant-to-water ratio equal to unity and constant temperature of 21 degrees C. The transformation from a normal hexagonal to a lamellar phase is observed as a function of increasing polymer content. The small-angle X-ray scattering results demonstrate the presence of a well-defined hexagonal structure up to about 1 wt % of polymer content that transforms into a lamellar structure at 7.7 wt % of polymer, as evidenced by two harmonics present in the scattering spectrum. There is no two-phase region observed. Freeze fracture electron microscopy images demonstrate the presence of a hexagonal phase up to the polymer concentration of 1.0 wt % and a lamellar phase for higher polymer concentrations (1.6 wt % and above). The polymer molecules are confined inside the surfactant bilayers of a lamellar phase. The textures seen using polarizing microscopy provide a strong supportive argument for a gradual change of topology with the addition of polymer.