We propose two possible new compounds, Ba2CuO2Fe2As2 and K2CuO2Fe2Se2, which hybridize the building blocks of two high temperature superconductors, cuprates and iron-based superconductors. These compounds consist of square CuO2 layers and antifluorite-type Fe2X2 (X=As, Se) layers separated by Ba/K. The calculations of binding energies and phonon spectra indicate that they are dynamically stable, which ensures that they may be experimentally synthesized. The Fermi surfaces and electronic structures of the two compounds inherit the characteristics of both cuprates and iron-based superconductors. These compounds can be superconductors with intriguing physical properties to help to determine the pairing mechanisms of high Tc superconductivity.