  We give the first (as far as we know) complete description of the boundary of
the Milnor fiber for some non-isolated singular germs of surfaces in ${\bf
C}^3$. We study irreducible (i.e. $gcd (m,k,l) = 1$) non-isolated (i.e. $1 \leq
k < l$) Hirzebruch hypersurface singularities in ${\bf C}^3$ given by the
equation $z^m - x^ky^l = 0$. We show that the boundary $L$ of the Milnor fiber
is always a Seifert manifold and we give an explicit description of the Seifert
structure. From it, we deduce that :
  1) $L$ is never diffeomorphic to the boundary of the normalization.
  2) $L$ is a lens space iff $m = 2$ and $k = 1$.
  3) When $L$ is not a lens space, it is never orientation preserving
diffeomorphic to the boundary of a normal surface singularity.
