The dispersion relationships in antiferromagnetically coupled magnonic crystals (MCs) were investigated using micromagnetic simulations. In contrast to traditional MCs, antiferromagnetically coupled MCs have two oppositely polarized modes, enabling the realization of synthetic ferrimagnetic and synthetic antiferromagnetic MCs. The magnon flatband effect was discovered, and a large bandgap of the dispersion relation was also realized in this structure. We found that the center frequency and width of the dispersion bands with a specific polarization were influenced by the thickness and thickness ratio of the spin-up and spin-down magnetic sublattices. Based on these results, spin-wave filtering devices were proposed. Our study uncovered the magnon dispersion relations of a type of MC, which provides fresh insights into the development of ultra-efficient magnonic devices.