In this paper, we consider a (p, q)-generalization of the r-Whitney-Lah numbers that reduces to these recently introduced numbers when p = q = 1. We develop a combinatorial interpretation for our generalized numbers in terms of a pair of statistics on an extension of the set of r-Lah distributions wherein certain elements are assigned a color. We obtain generalizations of some earlier results for the r-Whitney-Lah sequence, including explicit formulas and various recurrences, as well as ascertain some new results for this sequence. We provide combinatorial proofs of some additional formulas in the case when q = 1, among them one that generalizes an identity expressing the r-Whitney-Lah numbers in terms of the r-Lah numbers. Finally, we introduce the (p, q)-Whitney-Lah matrix and study some of its properties.