The coupled heat and mass transfer between two separated cocurrently flowing phases in vertical pipes is examined. A numerical approach based on the two-dimensional boundary layer equations is presented and validated with experiments available in literature. The effects of multicomponent diffusion interactions on the mass fraction profiles are demonstrated at the point of osmotic diffusion of one component during condensation of two components. The coupling of the concentration profiles increases with Reynolds number and leads to countercurrent gradients even at cocurrent concentration differences. The results agree well with available experimental data.