The phase diagram of the ternary dodecyltetraethylene glycol (C12E4)/benzyl alcohol/water system with a surfactant concentration of up to 0.2 M was determined. With an increase in the alcohol concentration, the sequence of the phases was L-alpha l, L-alpha/L-alpha h, L-3, and L-3/L. At low alcohol and surfactant concentrations, the anomalous lamellar phase L-alpha(+) also appeared. Upon comparing the phase sequence of the C12E4 ternary system with that of medium chain alkanols, we concluded that benzyl alcohol stabilizes the lamellar phase. The rheological study allowed us to establish the boundary between the L-alpha l and the L-alpha h, subregions. At intermediate alcohol concentration, a two-phase region (in which both phases coexist) formed in the phase diagram. There is a critical shear rate that induces the transition from extensive bilayers (L-alpha h) to vesicles (L-alpha l).