We report a phase diagram for a novel microemulsion that consists of oil and water and of 15% of a surfactant mixture of an anionic and a nonionic surfactant. The phase diagram shows an optically isotropic channel that passes from the water-rich side to the oil-rich side. In contrast to the isotropic channel in microemulsions of nonionic surfactants, the reported system undergoes an abrupt transition of the structure in the isotropic channel with increasing oil content. The structural transition is reflected in the conductivity and the viscosity of the channel. Between the L(3) phase and the sample with 6% of oil the conductivity decreases 3 orders of magnitude. Thus, the bicontinuous structure at the origin of the channel transforms already with 6% of oil to a w/o structure. The viscosity shows a strong maximum at the transition. The w/o structures with low oil content were successful directly imaged by cryo-TEM. It can be seen that water is contained inside a polyhedral foam-like structure, where the polyhedral film is formed of the oil and the surfactant. The dimensions of the polyhedra are in the range of 20-100 nm. We call this structure "high internal phase microemulsion" (HIPME).