  In continuum thermodynamics, models of two-phase mixtures typically obey the
condition of pressure equilibrium across interfaces between the phases. We
propose a new non-equilibrium model beyond that condition, allowing for
microinertia of the interfaces, surface tension, and different phase pressures.
The model is formulated within the framework of Symmetric Hyperbolic
Thermodynamically Compatible equations, and it possesses variational and
Hamiltonian structures. Finally, via formal asymptotic analysis, we show how
the pressure equilibrium is restored when fast degrees of freedom relax to
their equilibrium values.
