Motivated by the melting transition of DNA, we study genuinely three-dimensionalmodels for two interacting open, flexible and homogeneous macromolecularchains, bound or unbound to each other, at thermal equilibrium fromabout room temperature up to about the denaturation temperature(Tun). In each chain, angular constraints on bond angles (due tocovalent bonding) determine monomers: each monomer containsne nucleotides and hasan effective length de. These monomers could remain practically unaltered for temperatures in a range above and belowTun, down to 300 K.Estimates for ne and de are provided and justified. Upon proceeding from Quantum Mechanics to theclassical limit and using suitable large-distance approximations (partly, due tothose monomer configurations), we get a generalization of Edwards’ model, whichincludes effective potentials between monomers. The classical partition function forthe two-chain system is reduced to an integral of a generalized and discretizedtwo-chain Green’s function. We analyse conditions for the denaturing transition.The fact that each single chain is an extended one-dimensional system modifiestheir mutual global interaction, in comparison with typical potentials betweennucleotides: this is simply illustrated by computing a global effective potentialbetween the two chains. Applications for Morse potentials are presented. Ourmodels seem to be physically compatible with some previous one-dimensional onesand could allow us to efficiently extend the latter to three spatial dimensions.