A new class of thermoplastic elastomers possessing unusual mechanical properties has recently been discovered in binary blends of A-b-(B-b-A′)n miktoarm star block copolymers and A homopolymers that spontaneously form an unusual, thermodynamically stable, aperiodic “bricks-and-mortar” (B&M) mesophase morphology. The B&M mesophase is believed to be stabilized by thermal fluctuations as in the well-known case of the bicontinuous microemulsion phase. Here, two-dimensional field-theoretic simulations are used to study the equilibrium self-assembly of such miktoarm polymer binary blends. As expected, the B&M mesophase is not present in the mean-field phase diagram obtained with self-consistent field theory, but complex Langevin (CL) simulations, which fully incorporate thermal fluctuation effects, reveal dramatic changes to the phase diagram. A region of strong fluctuations results in the emergent stabilization of the B&M mesophase in a broad composition channel positioned between microphase separation and macrophase separation envelopes, consistent with experimental observations. Our simulations clarify the topology of the blend phase diagram and suggest that the B&M mesophase, at least as observed near the order−disorder transition, has no long- range or quasi-long-range positional or orientational order.