We study adsorption of a symmetric binary Lennard-Jones mixture, which exhibits partial mixing in a bulk phase, in slitlike pores formed by the walls having antisymmetric properties with respect to the components. The calculations are carried out by means of a density functional approach. We show that under suitable conditions the pore filling may occur as a sequence of two first-order transitions. The capillary condensation may lead to an "antisymmetric" liquidlike film, the symmetry of which follows the symmetry of the adsorbing potential, or to a "demixed" film, the symmetry of which is only weakly associated with the symmetry of the adsorption potential. The additional first-order antisymmetric-demixed film transition begins at the triple point temperature and ends at the critical end point temperature.