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)\leq 2 , for all primes p . Moreover, \beta_{p}(\mathcal A)=0 if p>3 , and \beta_{2}(\mathcal A)\neq 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)\neq 0 , for 2\leq d\leq 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.