Direct evidence by cryogenic temperature transmission electron microscopy shows the existence of networks in microemulsions near the two-phase closed loops. Networks formed by interconnected oil-swollen cylinders were observed in the water-rich regions of the phase diagram of the C12E5/water/n-octane system. The coexisting phases within the loops were shown to be concentrated and dilute networks. Similar micellar networks were also found in the binary system. These observations substantiate the suggested theoretical link between the structural bicontinuity and the unique phase separation and criticality of microemulsions: All these regimes are governed by the entropic attraction between network junctions.