We discuss an application of a density functional approach to describe a bilayer, or a simplified model of a membrane, that is built of tethered chain molecules. The bilayer integrity is maintained by tethering chain particles to two common sheets. We study the structure of a two-component mixture in contact with the bilayer, as well as the solvation force acting between two bilayers, immersed in a fluid. The fluid is a binary mixture involving the component that can cross freely the bilayer and the second impenetrable component. All the calculations are carried out for athermal system, in which only hard-core interactions are present.