Polymeric bicontinuous microemulsions are thermodynamically stable structures typically formed by ternary blends of immiscible A and B homopolymers and a macromolecular surfactant such as an AB diblock copolymer. Investigations of these bicontinuous morphologies have largely focused on model systems in which all components have narrow molecular weight distributions. Here we probe the effects of AB diblock polydispersity in ternary blends of polystyrene (PS), polyisoprene (PI), and poly(styrene-b-isoprene) (PS-PI). Three series of blends were prepared using the same PS and PI homopolymers; two of them contain nearly monodisperse components while the third includes a polydisperse PS-PI diblock. The PS and PI homopolymers and two of the PS-PI diblocks were prepared by anionic polymerization using sec-butyllithium and have narrow molecular weight distributions. The polydisperse PS-PI diblock was prepared by anionic polymerization using the functional organolithium 3-tert-butyldimethylsilyloxy-1-propyllithium; this diblock has a polydisperse PS block (Mw/Mn = 1.57) and a nearly monodisperse PI block (Mw/Mn < 1.1). The phase behavior of the three series of blends was probed using a combination of dynamic mechanical spectroscopy, small-angle X-ray scattering, and cloud point measurements, and a bicontinuous microemulsion channel was identified in each system. These results prove that monodisperse components are not required to form bicontinuous microemulsions and highlight the utility of polydispersity as a tool to tune polymer blend phase behavior. The random-phase approximation, originally advanced by de Gennes, and self-consistent field theory are used to provide a theoretical supplement to the experimental work. These theories are able to predict the directions of the polydispersity-driven shifts in domain spacing, order-disorder transition temperatures, and the location of the microemulsion channel. Self-consistent field theory is also used in conjunction with the experimental data from a series of nearly monodisperse blends to probe the variations of chi with temperature. A single linear relation of the form chi = alpha/T + beta does not describe chi at all blend compositions. Rather, two separate relations describe chi as a function of temperature; one is obtained from data on the diblock-rich side of the bicontinuous microemulsion channel while the other is obtained from data on the homopolymer-rich side of the channel. The blend morphology, rather than the composition (homopolymer fraction), apparently dictates whether the system is in the "diblock chi" or "homopolymer chi" regime. These results reinforce the notion that a true understanding of chi still eludes the polymer science community.