A class of phenolphthalein anilide (PA)-based poly(ether sulfone) multiblock copolymers containing pendant quaternary ammonium (QA) and imidazolium (IM) groups were synthesized and evaluated as anion exchange membrane (AEM) materials. The AEMs were flexible and mechanically strong with good thermal stability. The ionomeric multiblock copolymer AEMs exhibited well-defined hydrophobic/hydrophilic phase-separated morphology in small-angle X-ray scattering and atomic force microscopy. The distinct nanophase separated membrane morphology in the AEMs resulted in higher conductivity (IECw = 1.3–1.5 mequiv./g, σ(OH⁻) = 30–38 mS/cm at 20 °C), lower water uptake and swelling. Finally, the membranes were compared in terms of microbial fuel cell performances with the commercial cation and anion exchange membranes. The membranes showed a maximum power density of ~310 mW/m² (at 0.82 A/m²); 1.7 and 2.8 times higher than the Nafion 117 and FAB-PK-130 membranes, respectively. These results demonstrated that the synthesized AEMs were superior to Nafion 117 and FAB-PK-130 membranes.