We study the crystalline and interface structure of RBa2Cu3O7/La1−xAxMnO3 superlattices (R=Y, Gd; A=Ca, Sr) grown on mismatched MgO substrates by means of nondestructive x-ray diffraction. The diffraction patterns are adjusted to a model of the structure which includes interface roughness and interdiffusion. Our results show that these disorder mechanisms cannot be neglected and should be taken into account to understand the physical properties of these superlattices.