We study two-component vesicles with coherent domains of the components, where the domains are separated by an interface. The components are characterized by different spontaneous curvatures. No line tension term or interactions between components are included in the model. The influence of the interface width and interface location on the bending energy and shape of the vesicles is studied. How the spontaneous curvature of one component influences the concentration profile is examined. The vesicles of oblate and prolate geometries are investigated.