A new family of heterostructured transition-metal dichalcogenides (TMDCs) with incommensurate (“misfit”) spatial arrangements of well-defined layers was prepared from structurally dissimilar single-phase 2H-MoS2 and 1T-HfS2 materials. The experimentally observed heterostructuring is energetically favorable over the formation of homogeneous multi-principle element dichalcogenides observed in related dichalcogenide systems of Mo, W, and Ta. The resulting three-dimensional (3D) heterostructures show semiconducting behavior with an indirect band gap around 1 eV, agreeing with values predicted from density functional theory. Results of this joint experimental and theoretical study open new avenues for generating unexplored metal-dichalcogenide heteroassemblies with incommensurate structures and tunable physical properties.