The hydrated morphology of either proton exchange membranes (PEMs) or anion exchange membranes (AEMs) determines many aspects of species transport. The present work seeks to understand the morphology and microstructure of a triblock copolymer, polystyrene-b-poly(ethylene-co-butylene)-b-polystyrene (SEBS), functionalized with alkyl-substituted quaternary ammonium groups. Mesoscale dissipative particle dynamics (DPD) simulations were utilized and parametrized by reproducing the experimental morphology of the SEBS copolymer. It was found that the AEM (i.e., quaternary ammonium-functionalized SEBS) phase separates into a functionalized polystyrene-rich phase that is hydrophilic and a hydrophobic phase consisting of the SEBS mid-blocks. The morphology was controlled by the water content and was transformed from perforated and interconnected lamellae to perfect lamellae and then to disordered bicontinuous domains by increasing the hydration level (lambda = H2O/functional head group) from 4 to 20. The hydrophilic phase swelled upon the hydration of the membrane consistent with AFM phase imaging of a similar SEBS-based ionomer. Domains exclusively consisting of water were formed at high levels of hydration (lambda = 16 and 20) within the hydrophilic phase. Changing the anion from OH- to Cl- resulted in larger water domains at the highest hydration levels.