We have investigated the microstructure and rheological properties of ternary surfactant mixtures in a salt solution. The surfactants were 6% sodium 4-dodecylbenzenesulfonate, 3% C13-15 ethoxylated alcohol with seven ethylene oxide (EO) units and 1% C13-15 ethoxylated alcohol with 2, 4, 7, 9, 11, 14, 20, or 25 EO units. The salt solution was 10% nitrilotriacetate·H2O. Microstructural investigations (electron microscopy, light microscopy, confocal laser microscopy, conductivity measurements, and centrifugation) show that at rest the samples containing the surfactant with 2 EO to 9 EO units are dispersions of lamellar droplets (curved surfactant bilayers). The samples containing the surfactant with 11 EO to 25 EO units show a continuous lamellar structure (sheets of surfactant bilayers) with a small amount of lamellar droplets present. The change in several rheological parameters reflects this change in microstructure. The power law index from flow experiments at low shear rates changes from 0.1 for the lamellar dispersions to 0.4 for the continuous lamellar phases. Similar changes are observed in shear modulus and in the limiting strain for linear viscoelastic behavior. The continuous lamellar phase is converted to droplets by shearing at rates above 1 s-1. The continuous lamellar structures will recover in about a week when the samples are allowed to relax. The nature of the droplets is highly dynamic. Confocal laser microscopy shows small fluctuations in droplet shape on a time scale of about 100 s. This time coincides with a characteristic time of around 100 s pertaining to a (shallow) peak in G''.