With increasing hopes placed on the Na-ion battery technology to complement the current Li-ion battery systems, it is important to improve the energy density of Na-based cathode materials. Na-rich rocksalt oxides, Na1+xM1-xO2 (M = transition metal), combining cationic and anionic redox activity, could provide the necessary increase in capacity to achieve this goal, but their synthesis remains challenging compared to the Li analogues. As an alternative, mixed compounds Na(A(x)M(1-x))O-2, with A being an electropositive cation such as Li, Mg, or Zn sitting in the transition-metal layer, have been reported. As a continuation, we herein prepared the mixed Na(Li1/3Ir2/3)O-2 phase and compared its structure and electrochemical properties with the well-known Li2IrO3 and Na2IrO3 parent materials. By mixing Na and Li in the material, the stacking sequence of the transition-metal honeycomb layers in Na(Li1/3Ir2/3)O-2 is modified compared to the two parent materials, resulting in the presence of extra superstructure peaks in X-ray diffraction data. Using electrochemical characterization and an in-situ X-ray diffraction technique, the mixed Na(Li1/3Ir2/3)O-2 was found to be unstable both in Li and Na batteries and to separate into Na-rich Na-x IrO3 and Li-rich LixIrO3 phases due to the competition between electrochemical (de)insertion, cation exchange with the electrolyte, and segregation of Na and Li in the material. These findings highlight important challenges and offer useful insight into guide the design of new mixed Na(A(x)M(1-x))O-2 cathode materials with high capacity for Na-ion batteries.