A model is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of types AA, BB, and AB. Neighboring molecular ends have three-body and orientation-dependent interactions. The model is shown to be equivalent to a spin-1/2 Ising model on the same lattice with a field, but with only pairwise interactions. Symmetric and asymmetric coexistence surfaces for the separation into an AA-rich and a BB-rich phase are calculated exactly. (C) 2004 American Institute of Physics.