In partially ionized, magnetically confined plasmas, the diffusive fluxes of different species are coupled. Additionally, the fluxes are directionally coupled due to the Lorentz force. The challenge in the modelling of multi-component, magnetized plasmas is to take care of this coupling in the numerical method. In this paper, a complex form of the Stefan–Maxwell equations is used to account for the coupling between the flow directions. To handle the coupling between the species fluxes in the finite volume method, a generalized, coupled form of the exponential scheme is used. The presented numerical method is applied to a magnetically confined hydrogen jet. The results show that the numerical method is capable of describing typical characteristics of magnetized plasmas, such as anisotropic diffusion and the presence of a pressure gradient sustained by the Lorentz force.