  We study the quark-hadron mixed phase in proto-neutron stars with the
finite-size effects. In the calculations of pasta structures appeared in the
mixed phase, the Gibbs conditions require the pressure balance and chemical
equilibrium between two phases besides the thermal equilibrium. We find that
the region of the mixed phase is limited due to thermal instability. Moreover,
we study the effects of neutrinos to the pasta structures. As a result, we find
that the existence of neutrinos make the pasta structures unstable, too. These
characteristic features of the hadron-quark mixed phase should be important for
the middle stage of the evolutions of proto-neutron stars.
