  We introduce a generalization of the Stirling numbers via symmetric functions
involving two weight functions. The resulting extension unifies previously
known Stirling-type sequences with known symmetric function forms, as well as
other sequences such as the $p,q$-binomial coefficients. Recurrence relations,
generating functions, orthogonality relations, convolution formulas, and
determinants of certain matrices involving the obtained sequences are derived.
We also give combinatorial interpretations of certain cases in terms of colored
partitions and permutations.
