A detailed study of hole-particle distributions in many-electron molecular systems is presented, based on a representation of the high-order density matrices obtained by an operator technique reminiscent of Bogolyubov's quantum statistical operator theory. A rigorous definition of density matrices of arbitrary order is given for a composite system of holes and particles. Particular attention is focused on the description of mixed hole-particle distributions. The main results are given as the functionals of excitation operators (generators) that are used in the conventional configuration interaction (CI) and coupled cluster (CC) theories. Local atomic occupation numbers for holes and particles are introduced to provide a measure of the participation of specific atoms in the electron correlation processes. The corresponding total occupations--as well as the hole-hole, particle-particle, and hole-particle mean distances--provide a useful and physically intuitive description of electron correlation. Suitable computational schemes for numerical evaluation of the above characteristics within full CI and typical CC approaches are presented. The insights one can gain with the developed approach into the peculiarities and nuances of the hole-particle picture in typical electronic processes such as excitation and molecular dissociation are illustrated with specific computations on small molecules and closed-shell atoms.