The many similarities in morphological behavior exhibited by diblock copolymer melts and lyotropic surfactant suspensions suggest the existence of common physical principles underlying these phenomena. In an effort to identify such principles, we discuss the phase behavior of aqueous solutions of poly(ethylene oxide)-poly(ethylethylene) (PEO-PEE) block copolymers. The molecular weights of these materials are roughly twice that of common poly(ethylene oxide)-poly(propylene oxide) (PEO-PPO) surfactants, leading to microphase separation and a rich mesophase polymorphism in the absence of solvent. Despite the strongly thermotropic nature of the PEO-water interaction, the phase behavior in solutions of high polymer concentration is primarily lyotropic. Mesophase transitions observed in this regime show characteristics similar to those observed in undiluted block copolymers. A crossover to thermotropic behavior occurs at concentrations on the order of 60 wt % polymer, which corresponds to the formation of a stoichiometric complex of three water molecules per ethylene oxide repeat. This crossover is accompanied by changes in the structural dimensions, long-range order, and mechanical characteristics of the mesophases. Transitions in these dilute solutions resemble those previously observed in surfactant systems. These findings suggest that the complex structure of hydrated PEO plays a central role in determining the phase behavior of the system.