  We study coherence and entanglement properties of the state space of a
composite bi-fermion (two electrons pierced by $\lambda$ magnetic flux lines)
at one Landau site of a bilayer quantum Hall system. In particular, interlayer
imbalance and entanglement (and its fluctuations) are analyzed for a set of
$U(4)$ coherent (\emph{quasiclassical}) states generalizing the standard
pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay
between spin and pseudospin degrees of freedom opens new possibilities with
regard to the spin-frozen case. Actually, spin degrees of freedom make
interlayer entanglement more effective and robust under perturbations than in
the spin-frozen situation, mainly for a large number of flux quanta $\lambda$.
Interlayer entanglement of an equilibrium thermal state and its dependence with
temperature and bias voltage is also studied for a pseudo-Zeeman interaction.
