We discuss the position of lattice hole theories in the original Simha-Somcynsky formulation and modifications by Nies, Stroeks and Xie, as applied to a series of mixed systems, of the intermolecular as well as the intramolecular type. The former encompass molecular mixtures of low and high molar mass constituents, and also composites. The latter include statistical copolymers as well as oligomers with their distinctive terminal and internal constituent groups. An important ingredient of these theories is the temperature and volume dependent hole fraction, obtained by the minimization of the configurational free energy. It has the character of a free volume quantity and is shown to bear a close relation to the free volume fraction extracted from positron probe spectroscopy. Its importance is implicit in the above applications. It is explicit in problems of phase relations and in correlations between surface tension and bulk properties of polymer and oligomer melts. Its significance for transport processes in the melt was pointed out by Utracki, and subsequently for viscoelastic processes in melt and glass, by several authors.