The model polymeric bicontinuous microemulsion under study exhibits four regimes as a function of the shear rate. Regime I resembles conventional Newtonian fluids. In regime II, there is an onset of anisotropy and shear thinning. Unlike the surfactant sponge phase, there is no transition to lamellar phase, instead the system undergoes phase separation upon entering regime III. The stress is independent of the shear rate, and this stress plateau resembles the behavior of worm-like micelles. There is complete phase separation in regime IV and the rheological properties become similar to those of binary polymer blends. We have thus established that polymeric bicontinuous microemulsions possess rich rheological behavior within accessible shear rates, and hence can serve as excellent model systems for studying the rheology and dynamics of this class of complex fluids.