  We consider a $(q,y)$-analogue of Laguerre polynomials
$L^{(\alpha)}_n(x;y;q)$ for integral $\alpha\geq -1$, which turns out to be a
rescaled version of Al-Salam--Chihara polynomials. A combinatorial
interpretation for the $(q,y)$-Laguerre polynomials is given using a colored
version of Foata-Strehl's Laguerre configurations with suitable statistics.
When $\alpha\geq 0$, the corresponding moments are described using certain
classical statistics on permutations, and the linearization coefficients are
proved to be a polynomial in $y$ and $q$ with nonnegative integral
coefficients.
