We consider a lattice model of a binary mixture in which each molecule of one component can form zero, one, or two bonds to molecules of the same species on neighboring vertices of the square lattice. We allow the energy of molecules with two bonds to depend on the valence angle, thus generalizing the first paper in this series. If straight polymeric configurations are favored over all others, then a phase transition occurs for low enough temperature. On the other hand, if bent configurations are favored, there is no phase transition. Analogous results are obtained for the hexagonal lattice, where we distinguish energetically betweencis andtrans isomerism of four bonded molecules.