Asymmetric building blocks afford assembly of more complex, sophisticated materials than their homogeneous counterparts. Phase separation of mixed membranes produces asymmetric surface textures in lipid vesicles. Membranes that demix into coexisting liquid phases ripen such that the vesicle domain morphology exhibits a Janus-like texture. DNA is commonly used in material science as a molecular glue. Hydrophobically modified DNA strands anchor to the membranes of vesicles such that the DNA is free to bind its complement. When DNA amphiphiles are anchored to phase separated vesicles, they thermodynamically partition between coexisting domains. This results in asymmetric surface distributions of adhesive functionalities. We enhance the partitioning of cholesteryl-anchored DNA into liquid ordered (L-o) domains of Janus-like vesicles by incorporating highly unsaturated lipids into membrane mixtures. We find that cardiolipin (CL) drives the strongest enrichment of DNA into L-o domains with apparent surface concentrations at least an order of magnitude greater than in coexisting liquid disordered domains. We also examine the partitioning of DNA with a lipid-like anchor in Janus-textured vesicles; the inclusion of CL also drives a very strong enhancement into L-o domains. The culmination of this work is the study of superstructures that form when populations of these Janus vesicles, functionalized by complementary DNA strands, are mixed. Unlike their homogeneous counterparts, which can form uncontrollably large clusters, size-limited multicompartmental architectures are observed. The DNA-rich L-o domains saturate in adhesion plaques of the clusters. This predominantly leaves DNA-depleted L-alpha phase accessible on the exterior surface of these structures, which does not favor binding of further vesicles.