Monolayers of linear and miktoarm star ABC triblock copolymers with equal A and C blocks were investigated using self-consistent field theory. Monolayers of ABC triblock copolymers were formed between two parallel surfaces that were attractive to the A and C blocks. The repulsive interaction parameter chi N-AC between the A and C blocks was chosen to be weaker than the A/B and B/C interactions, quantified by chi N-AB and chi N-BC, respectively, such that the B blocks were confined at the A/C interface, resulting in various B domains with different geometries and arrangements. It was Observed that two variables, namely, the strength of the surface fields and the film thickness, were dominant factors controlling the self-assembly of the B blocks into various morphologies. For the linear triblock copolymers, the morphologies of the B domains included disks, stripes (parallel cylinders), and hexagonal networks (inverse disks). For the miktoarm star triblock copolymers, the competition between the tendency to align the junction points along a straight line and the constraint on their arrangement from the surface interactions led to richer ordered morphologies. As a result of the packing of the junction points of the ABC miktoarm star copolymers, a counterintuitive phase sequence from low-curvature phases to high-curvature phases with increasing length of B block was predicted. The study indicates that the self-assembly of monolayers of ABC triblock copolymers provides an interesting platform for engineering novel morphologies.