Lyotropic mixtures of rodlike and flexible polymers are studied. The rodlike polymer is modelled by a hard rod and the flexible polymer by a self-avoiding walk. The interaction between rodlike and flexible polymers is studied and a tendency for this interaction to force demixing is found. Diameters of the rod which are much larger than the diameter of the segments of the flexible polymer but much smaller than its radius of gyration are considered because of their relevance to mixtures of helical biopolymers and flexible polymers.