The number of atomic layers confined in a two-dimensional structure is crucial for the electronic and magnetic properties. Single-layer and bilayer J_{eff}=1/2 square lattices are well-known examples where the presence of the extra layer turns the XY anisotropy to the c-axis anisotropy. We report on experimental realization of a hybrid SrIrO_{3}/SrTiO_{3} superlattice that integrates monolayer and bilayer square lattices in one layered structure. By synchrotron x-ray diffraction, resonant x-ray magnetic scattering, magnetization, and resistivity measurements, we found that the hybrid superlattice exhibits properties that are distinct from both the single-layer and bilayer systems and cannot be explained by a simple addition of them. In particular, the entire hybrid superlattice orders simultaneously through a single antiferromagnetic transition at temperatures similar to the bilayer system but with all the J_{eff}=1/2 moments mainly pointing in the ab plane similar to the single-layer system. The results show that bringing monolayer and bilayer with orthogonal properties in proximity to each other in a hybrid superlattice structure is a powerful way to stabilize a unique state not obtainable in a uniform structure.