We study the phase behavior of diblock copolymers in a curved bilayer. Three aspects are discussed in detail: domain size distributions of the two adjacent monolayers within the film, optimal film thickness for a bilayer, and structural transition from a monolayer to a bilayer. One major finding is the determination of transition point in film thickness where the layer-type structure goes from monolayer to bilayer. At high confinement, the transition point increases as the curvature increases regardless of the symmetry of diblock copolymers. At low confinement, the transition point might increase or decrease, depending on the symmetry of diblock copolymers. (C) 2015 Elsevier B.V. All rights reserved.