The interplay between the ion exchange capacity, water content and concentration dependences of conductivity, diffusion permeability, and counterion transport numbers (counterion permselectivity) of CJMA-3, CJMA-6 and CJMA-7 (Hefei Chemjoy Polymer Materials Co. Ltd., China) anion-exchange membranes (AEMs) is analyzed using the application of the microheterogeneous model to experimental data. The structure-properties relationship for these membranes is examined when they are bathed by NaCl and NaSO solutions. These results are compared with the characteristics of the well-studied homogenous Neosepta AMX (ASTOM Corporation, Japan) and heterogeneous AMH-PES (Mega a.s., Czech Republic) anion-exchange membranes. It is found that the CJMA-6 membrane has the highest counterion permselectivity (chlorides, sulfates) among the CJMAED series membranes, very close to that of the AMX membrane. The CJMA-3 membrane has the transport characteristics close to the AMH-PES membrane. The CJMA-7 membrane has the lowest exchange capacity and the highest volume fraction of the intergel spaces filled with an equilibrium electroneutral solution. These properties predetermine the lowest counterion transport number in CJMA-7 among other investigated AEMs, which nevertheless does not fall below 0.87 even in 1.0 eq L solutions of NaCl or NaSO. One of the reasons for the decrease in the permselectivity of CJMAED membranes is the extended macropores, which are localized at the ion-exchange material/reinforcing cloth boundaries. In relatively concentrated solutions, the electric current prefers to pass through these well-conductive but nonselective macropores rather than the highly selective but low-conductive elements of the gel phase. It is shown that the counterion permselectivity of the CJMA-7 membrane can be significantly improved by coating its surface with a dense homogeneous ion-exchange film.