Self-assembly can easily produce intricate structures that would be difficult to make by conventional fabrication means. Here, self-assembly is used to prepare multicomponent polymeric microspheres of arbitrary internal symmetries. Droplets of liquid prepolymers are printed onto a water-soluble hydrogel, and are allowed to spread and coalesce into composite patches. These patches are then immersed in an isodense liquid, which both compensates the force of gravity and dissolves the gel beneath the polymers. Subsequently, the patches fold into spheres whose internal structures are dictated by the arrangement of the droplets printed onto the surface. The spheres can be solidified either thermally or by ultraviolet radiation. We present a theoretical analysis of droplet spreading, coalescence and folding. Conditions for the stability of the folded microspheres are derived from linear stability analysis. The composite microbeads that we describe are likely to find uses in optics, colloidal self-assembly and controlled-delivery applications.