Textured TlBaCaCuO superconducting thin films identified by electron microscopy as consisting of a mixture of TlBa2Ca2Cu3O9and Tl2Ba2Ca2Cu3O10layers with no long range crystalline order normal to the basal planes have been prepared. The Tl1+xBa2Ca2Cu3O9+xthin films yield complex x‐ray diffraction patterns with a nonrational series of basal reflections. In order to further understand the structure of this material, a statistical model for x‐ray diffraction by partially disordered layered structures was formulated for a material consisting of a random mixture of two types of layers in which both the layer thickness and scattering power of the layers differ. The scattering equation was solved computationally for x‐ray scattering from the basal planes of layered materials consisting of random mixtures of TlBa2Ca2Cu3O9and Tl2Ba2Ca2Cu3O10layers. The results were applied to the modeling of the x‐ray diffraction scattering intensity for 1.0‐&mgr;m‐thick textured thin films of TlBa2Ca2Cu3O9, Tl2Ba2Ca2Cu3O10, and Tl1+xBa2Ca2Cu3O9+x. The computational results support the identification of one such Tl1+xBa2Ca2Cu3O9+xthin film as consisting predominantly of a nearly random mixture of 50% TlBa2Ca2Cu3O9and 50% Tl2Ba2Ca2Cu3O10layers (x&bartil;0.5). The model was also used to examine the effect of intergrowth layers in TlBaCaCuO compounds on the intensity, location, and width of the basal plane reflections.