We study the effect of curvature on chiral membranes with interactions that favor alignment with  the local surface normal. Unlike many other previously studied cholesteric surfaces, such membranes have an in-plane pitch axis, as opposed to one normal to the plane. The aligning interaction is mathematically equivalent to a magnetic field locally normal to the surface, and hence we expect a transition from a cholesteric to an aligned phase at a finite interaction strength, as pointed out by Meyer and deGennes. Starting with the directors  confined to a fixed cylindrical geometry, we numerically determine the tilt angle of the directors relative to the normal, as a function of the pitch and the interaction strength. We find evidence of the aligning transition, along with additional effects due to the curvature of the surface. We also present a theoretical model that predicts the behavior determined by the numerical analysis, including  the structure of the observed pi-walls. Finally, to probe the effect of intrinsic curvature, we study unduloid-shaped membranes that allow a continuous increase of Gaussian curvature from a cylinder to a sphere. Our work systematically elucidates the effect of domain curvature on chiral membranes.