We develop a model to probe the relative orientation of two second-order polarizable daunomycin molecules that are intercalated into a DNA duplex using optical second-harmonic (SH) generation. The SH field generated by the daunomycin molecules interfere with each other. Because the interference depends on the relative orientation of the daunomycin molecules, we can control the interference by changing the number of base pairs separating them. The relative orientation changes as the number of base pairs separating them, multiplied by 36 degrees, which is the twist angle between neighboring base pairs. In this paper, we derive a set of relationships between the relative angle of the molecules and the nonlinear susceptibility elements, and we calculate the SH field generated by the DNA/molecular-pair complex attached to an isotropic dielectric sphere. Calculations reveal that the SH intensity varies periodically with the relative orientation of the two chromophores in the plane perpendicular to the helical axis. The predicted periodicity is in close agreement with experimental results. Structural changes induced by foreign molecules binding to DNA will change the relative orientation of the two chromophores and thereby change the SH interference pattern. We discuss the potential of this SH interference method in providing a new way to probe structural changes induced by the formation of biomolecule complexes. An important feature of the method is that it is label-free, that is, the binding molecule, in this case, daunomycin, is not tagged.