The formation of a capillary phase in segregating mixed polymer solutions confined between two planar walls is modeled by using a lattice mean-field theory for flexible polymers in solution. A capillary-induced phase separation (CIPS) may appear in systems where the two polymer components display different preference for the wall, the preference being either of energetic or entropic origin. A long-range attractive force operating between the walls across the polymer solution is associated with the CIPS. The CIPS phenomenon is discussed for two different polymer systems. The effects of the chain length asymmetry, the solution composition, and the interactions with the walls on the range and the magnitude of the attractive force are presented. For compositions near the binodal curve and far from the critical point, the attractive force is very long-ranged and its range exceeds far the dimension of the polymer chains. Polymer distributions between the walls at the onset of the attractive force in the systems are also reported.