We develop a statistical mechanical theory for the free energy landscapes for complexes of double-stranded chain molecules. The theory is based on the generalized polymer graph, a graphical representation for the conformations of the complexes. We compute the partition functions by "dividing and conquering" on the generalized polymer graph: we decompose a graph into simple subunits, calculate the partition function of each subunit exactly, and treat the interactions between subunits approximately, by calculating the localized interactions (of the nearest neighbor and the next-nearest neighbor monomers) at the interface of subunits. Our tests against the exact computer enumeration on the two-dimensional (2D) square lattice show that the theory is accurate. We apply the theory to the computation of the free energy landscapes of three representative systems: homopolymer-homopolymer, homopolymer-heteropolymer, and heteropolymer-heteropolymer complexes, using contact-based energy functions for the homopolymer-homopolymer and homopolymer-heteropolymer complexes, and stacking energies for the heteropolymer-heteropolymer complexes (to mimic RNA secondary structures). We find that the systems involving homopolymers show smooth free energy landscapes, and undergo noncooperative structural transitions during the melting process, and that the system of heteropolymers show rugged free energy landscapes, and the thermal denaturation involves intermediate states and cooperative structural transitions. We believe this approach maybe useful for computing the free energy landscapes and the thermodynamics of DNA or RNA interactions and RNA binding to a DNA or RNA target. (C) 2001 American Institute of Physics.