We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous particle pack at a rate proportional to the square of the droplet radius. By contrast, small droplets do not collapse, but remain intact and are merely deformed. A simple model coupling the Laplace pressure to Darcy's law correctly estimates both the threshold radius separating these two behaviors, and the rate of large-droplet evacuation. Finally, we use these systems to make novel hierarchical structures. The drying of suspensions of colloidal particles gives rise a plethora of fascinating phenomena, from the "coffee-ring" effect[1] to episodic crack propogation [2] and the fractal patterns arising from invasion percolation [3][4][5][6][7]. Drying of colloidal suspensions is also important technologically: paints and other coatings depend on colloidal particles for many of their key properties, many ceramics go through a stage of particle drying, and cosmetics often exploit the unique properties of colloidal-scale particles, particularly for such beneficial properties as screening the harmful effects of the sun. However, for many of these technological applications, the colloidal particles are but one of many different components, and drying of the colloids is accompanied by many other phase changes. While these mixtures can become highly complex, a simpler, yet still rich system that embodies many of the complex phenomena of these technological suspensions is a mixture of immiscible fluids with a colloidal suspension; a simple example is a mixture of an emulsion and colloidal particles. The behavior of the emulsion embodies many of the archetypal phenomena of such systems, while still remaining sufficiently tractable to enable it to be fully understood. However, emulsions themselves typically scatter light significantly, and when mixed with a colloidal suspension, this scattering is only enhanced. As a result, it is very difficult to image this mixture, precluding optical studies of its behavior, and knowledge of the actual behavior is woefully missing.In this Letter, we explore the drying of mixtures of aqueous emulsion droplets and spherical colloidal particles with confocal microscopy, which allows us to resolve the full 3D structure of these mixtures and their temporal dynamics. We find that the particles first jam into a solidified pack, throughout which emulsion drops are dispersed; a front of air then passes through the entire system. When this drying front reaches large emulsion droplets, the droplets unexpectedly collapse and their internal contents are forced into the pore space between the surrounding colloids, driven by an imbalance of pressures at the droplets' interfaces with air and with the solvent. By contrast, small droplets are deformed by the drying front, yet remain intact without bursting. By coupling the Laplace pressure with Darcy's la...