  We formulate a density functional theory that describes the phase behavior of
hard rods and depleting polymers, as realized in recent experiments on
suspensions of \emph{fd} virus and non-adsorbing polymer. The theory predicts
the relative stability of nematic droplets, stacked smectic columns, and a
recently discovered phase of isolated monolayers of rods, or colloidal
membranes. We find that a minimum rod aspect ratio is required for stability of
colloidal membranes and that collective protrusion undulations are the dominant
effect that stabilizes this phase. The theoretical predictions are shown to be
qualitatively consistent with experimental and computational results.
