A device involving mass exchangers with a permeable membrane inserted to divide the open duct into two subchannels for conducting double-pass laminar countercurrent operations under asymmetric wall mass fluxes, which results in a substantial improvement of the mass transfer, has been developed and investigated theoretically. The resultant partial differential equations for such a double-pass forced-convection mass transfer problem are referred to as conjugated Graetz problems and solved analytically in this work by using an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the inhomogeneous part. The theoretical predictions of mass transfer efficiency improvement in double-pass, parallel-plate mass exchangers are obtained by suitably adjusting the permeable membrane location. They are represented graphically and compared with the results from an open duct of a single-pass operation (without a permeable membrane inserted). The increment of power consumption is also discussed.