  For each complex central essential hyperplane arrangement $\mathcal{A}$, let
$F_{\mathcal{A}}$ denote its Milnor fiber. We use Tevelev's theory of tropical
compactifications to study invariants related to the mixed Hodge structure on
the cohomology of $F_{\mathcal{A}}$. We prove that the map taking each
arrangement $\mathcal{A}$ to the Hodge-Deligne polynomial of $F_{\mathcal{A}}$
is locally constant on the realization space of any loop-free matroid. When
$\mathcal{A}$ consists of distinct hyperplanes, we also give a combinatorial
description for the homotopy type of the boundary complex of any simple normal
crossing compactification of $F_{\mathcal{A}}$. As a direct consequence, we
obtain a combinatorial formula for the top weight cohomology of
$F_{\mathcal{A}}$, recovering a result of Dimca and Lehrer.
