  Generalizing previous work of Hora (1998) on the asymptotic spectral analysis
for the Hamming graph $H(n,q)$ which is the $n^{\mathrm{th}}$ Cartesian power
$K_q^{\square n}$ of the complete graph $K_q$ on $q$ vertices, we describe the
possible limits of the joint spectral distribution of the pair $(G^{\square
n},\overline{G}\vphantom{G}^{\square n})$ of the $n^{\mathrm{th}}$ Cartesian
powers of a strongly regular graph $G$ and its complement $\overline{G}$, where
we let $n\rightarrow\infty$, and $G$ may vary with $n$. This result is an
analogue of the bivariate central limit theorem, and we obtain in this way the
bivariate Poisson distributions and the standard bivariate Gaussian
distribution, together with the product measures of univariate Poisson and
Gaussian distributions. We also report a family of bivariate hypergeometric
orthogonal polynomials with respect to the last distributions, which we call
the bivariate Charlier-Hermite polynomials, and prove basic formulas for them.
This family of orthogonal polynomials seems previously unnoticed, possibly
because of its peculiarity.
