  We compute the combinatorial Aomoto-Betti numbers $\beta_p(\mathcal{A})$ of a
complex reflection arrangement. When $\mathcal{A}$ has rank at least $3$, we
find that $\beta_p(\mathcal{A})\le 2$, for all primes $p$. Moreover,
$\beta_p(\mathcal{A})=0$ if $p>3$, and $\beta_2(\mathcal{A})\ne 0$ if and only
if $\mathcal{A}$ is the Hesse arrangement. We deduce that the multiplicity
$e_d(\mathcal{A})$ of an order $d$ eigenvalue of the monodromy action on the
first rational homology of the Milnor fiber is equal to the corresponding
Aomoto-Betti number, when $d$ is prime. We give a uniform combinatorial
characterization of the property $e_d(\mathcal{A})\ne 0$, for $2\le d\le 4$. We
completely describe the monodromy action for full monomial arrangements of rank
$3$ and $4$. We relate $e_d(\mathcal{A})$ and $\beta_p(\mathcal{A})$ to
multinets, on an arbitrary arrangement.
