  We analyze a system of PDEs governing the interaction between two
compressible mutually noninteracting fluids and a shell of Koiter type
encompassing a time dependent 3D domain filled by the fluids. The dynamics of
the fluids is modelled by a system resembilng compressible Navier-Stokes
equations with a physically realistic pressure depending on densities of both
the fluids. In fact in the present article the dependence of the fluid pressure
on the densities is analogous to the ones considered in \cite{NovoPoko} (where
the authors deal with a bi-fluid system in a time independent smooth domain).
The shell constitutes the boundary of the fluid domain and it possesses a
non-linear, non-convex Koiter energy (of a quite general form). We are
interested in the existence of a weak solution to the system until the
time-dependent boundary approaches a self-intersection or the Koiter energy
degenerates. We first prove a global existence result when the adiabatic
exponents solve $\max\{\gamma, \beta\}>2$ and $\min\{\gamma,\beta\}>0,$ further
the densities are comparable and the structure involved is non-dissipative.
Next with the assumption that the structure is dissipative we extend our global
existence result to the critical case $\max\{\gamma,\beta\}\geq 2$ and
$\min\{\gamma,\beta\}>0.$ The result is achieved in several steps involving,
extension of the physical domain, penalization of the interface condition,
artificial regularization of the shell energy, added structural dissipation and
suitable limit passages depending on uniform estimates. In order to deal with
the bi-fluid system we generalize the almost compactness argument developed in
\cite{NovoPoko, Vasseur} to the case of time dependent domains with uniform
H\"{o}lder continuous boundaries. Moreover, the proof of such a compactness
result depends on the existence of renormalized continuity equation in time
dependent domains.
