We consider structures formed by one semiflexible polyelectrolyte (PE) and one oppositely charged sphere and calculate the interaction between two such complexes within the ground-state approximation, where the PE assumes its optimal configuration. Using parameters appropriate for DNA-histone systems, we find the second virial coefficient of inter-complex interactions to be negative for intermediate salt concentrations within the range where stable complexes are formed, in agreement with experiments. A simple screened monopole-dipole model reproduces these findings.