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The existence of cold clouds embedded into hot interstellar plasma provides one more evidence of an inhomogeneity of interstellar medium. Cold cloud is a region filled up with cold dense atomic hydrogen. Although being embedded into the hot plasma the clouds should have been quickly evaporated, they have a surprisingly long lifetime that could be explained by some peculiarities of the cloud-plasma interaction. It has been shown by Provornikova et al. (2011) that the resonant charge exchange of proton and H atoms could lead to the longer existence of the interstellar clouds. However, the magnetic field has been neglected in this model. The aim of this work is to examine how the presence of the magnetic field changes the cloud-plasma interface. We consider a one-dimensional flow of the two-fluid medium. An initial values problem is studied: at the initial time the left half-space consists of cold dense neutral hydrogens, and the right one is of fully-ionized quasi-neutral plasma. The components interact only due to the charge exchange process. We also take into account the influence of the magnetic field on the plasma motion. The evolution of the initial discontinuity depends on three dimensionless numbers: the initial ratio of the densities, the plasma beta and the ratio of the magnetic fields. The reason why in the case of the magnetic field the effects of the charge exchange process are no as strong as it was without it will be pointed out.