  Motivated by the experimental study of Tayebi et al. [Nature Mater. 11, 1074
(2012)] on phase separation of stacked multi-component lipid bilayers, we
propose a model composed of stacked two-dimensional Ising spins. We study both
its static and dynamical features using Monte Carlo simulations with Kawasaki
spin exchange dynamics that conserves the order parameter. We show that at
thermodynamical equilibrium, due to strong inter-layer correlations, the system
forms a continuous columnar structure for any finite interaction across
adjacent layers. Furthermore, the phase separation shows a faster dynamics as
the inter-layer interaction is increased. This temporal behavior is mainly due
to an effective deeper temperature quench because of the larger value of the
critical temperature, $T_{\rm c}$, for larger inter-layer interaction. When the
temperature ratio, $T/T_{\rm c}$, is kept fixed, the temporal growth exponent
does not increase and even slightly decreases as function of the increased
inter-layer interaction, as the system crosses-over from two to three
dimensions.
