  We study a two-phase free boundary problem in which the two-phases satisfy an
impenetrability condition. Precisely, we have two ordered positive functions,
which are harmonic in their supports, satisfy a Bernoulli condition on the
one-phase part of the free boundary and a two-phase condition on the collapsed
part of the free boundary. For this two-membrane type problem, we prove an
epsilon-regularity theorem with sharp modulus of continuity. Precisely, we show
that at flat points each of the two boundaries is $C^{1,1/2}$ regular surface.
Moreover, we show that the remaining singular set has Hausdorff dimension at
most $N-5$ as in the case of the classical one-phase problem, $N$ being the
dimension of the space.
