A new promising class of ordered block copolymer morphologies in thin films we call diamond-like morphologies (DLM) is theoretically described in detail. This class comprises the cubic morphologies possessing diamond symmetry Fd (3) over barm as well as its tetragonal and orthorhombic generalizations. The characteristic property of the DLM is that the corresponding percolation cluster contains both perpendicular and parallel (with respect to the substrate) intertwining channels, which is expected to improve noticeably the permeability efficiency of such quasi-isotropic morphologies as compared to the anisotropic lamellar and cylindrical ones. On the basis of both the weak segregation theory (WST) analytical consideration and self-consistent field theory (SOFT) numerical procedure, we find relationships between the microscopic parameters of the ternary ABC symmetric block copolymers of a specified composition and their morphology in thin films. The effects of confinement (film width) and the film walls selectivity are analyzed, and the corresponding phase diagrams are built. Our key theoretical prediction is that the way the selectivity is distributed over the film substrate makes a drastic difference in the selectivity influence on the various phases' stability. The homogeneous selectivity distribution enhances the parallel lamellae stability. On the contrary, a simple 1D (lamellar) selectivity modulation could (depending on the modulation period) enhance the DLM stability. The explicit recommendations are made how to facilitate the DLM stabilizing in real block copolymers. We address also the issue of spectral and 3D visual ways to identify the SCFT equations solutions in thin films as the DLM.