We investigate lattice relaxation and band structures of helical and alternating twisted trilayer WSe₂ and MoTe₂ using machine-learning force fields and large-scale ab initio calculations. Interference between the two bilayer moiré lattices generates a supermoiré lattice that, upon relaxation, reconstructs into a few dominant domain types with locally commensurate bilayer moiré lattices. Because the systems lack C_2z symmetry, domains otherwise related by this symmetry become energetically and topologically distinct, unlike in twisted trilayer graphene. Band structure calculations show that the topmost valence bands originate from the K (K') valleys and carry domain-dependent valley Chern numbers. The resulting supermoiré lattice hosts a mosaic of topologically inequivalent domains, offering a platform for exploring correlated and topological physics.