The equilibrium dynamics of a bicontinuous microemulsion composed of polystyrene, polyisoprene, and poly(styrene-block-isoprene) was characterized using rheology and X-ray photon correlation spectroscopy (XPCS). XPCS measurements, which probed dynamics at length scales comparable to the microemulsion domain size, show stretched-exponential relaxation of the dynamic structure factor and a wavevector-dependent Onsager coefficient. Values of the Onsager coefficient corresponding to zero wavevector (q = 0) and the peak of the static structure factor (q = q(max)) were independently used to test rheological predictions for bicontinuous microemulsions developed by Patzold and Dawson. The theory, which is based on a Landau-Ginzburg model, describes the shape of the relaxation spectrum and predicts the temperature dependence of the rheological properties quite well. However, for either case of the Onsager coefficient (at q = 0 and q = q(max)), the theory fails to predict the absolute values of the zero-shear viscosity and average relaxation time of the microemulsion. The results of this study highlight a need for the development of more sophisticated theory to describe the rheology of bicontinuous microemulsions.