  Using a two-dimensional version of the delta method, we establish an
asymptotic formula for the number of rational points of bounded height on
non-singular complete intersections of cubic and quadric hypersurfaces of
dimension at least $23$ over $\mathbb{F}_q(t)$, provided
$\text{cha}(\mathbb{F}_q)>3$. Under the same hypotheses, we also verify weak
approximation.
