The static structure of solutions of DNA fragments is investigated using integral equation theory. The solution is modeled as a four-component system with DNA molecules, bound counterions, free counterions, and coions, all of which are treated explicitly. Each DNA fragment is modeled as a shish-kebab chain with three kinds of sites, i.e., charged sites, neutralized (protonated) sites, and sites with bound counterions. The partial structure factors are obtained using a generalization of the polymer reference interaction model. The undetermined parameters in the model, namely the fraction of protonated and bound sites, are obtained by fitting theoretical predictions for the polymer-polymer and polymer-counterions structure factors to experimental data. It is found that a large majority of counterions is localized near the DNA molecules due to counterions binding and protonation. The bound counterions make a dominant contribution to the total scattering from counterion species. The best fit is obtained when each DNA molecule contains about 22% protonated sites and 53% counterion occupied sites, i.e., the effective DNA charge fraction is about 0.25. This DNA charge fraction is consistent with electrospray ionization and DNA titration experiments.