This paper presents a novel family of bivariate two-dimensional ( $$$ 2D $$$) $$$ q $$$-Hermite–based Appell polynomials, introducing their construction along with explicit examples to illustrate their structure. The study explores key mathematical properties of these polynomials, including explicit forms and determinant-based representations that provide a foundational understanding of their algebraic framework. Central to the discussion is the establishment of the monomiality principle, which forms a crucial basis for deriving several other properties. The paper also examines $$$ q $$$-recurrence relations and $$$ q $$$-difference equations, further highlighting the interplay between these properties and the underlying $$$ q $$$-Hermite–based framework. In addition, the findings are extended to special classes of bivariate $$$ 2D $$$ polynomials, namely the $$$ q $$$-Hermite–based Bernoulli, Euler, and Genocchi polynomials, demonstrating the broader applicability and versatility of the proposed approach. These results enrich the existing theory of $$$ q $$$-polynomials and provide new tools for analyzing and generalizing classical polynomial families in the context of $$$ q $$$-calculus.