Besides being model systems for studying biological processes in cell membranes, lipid vesicles offer promise as containers for use in technological applications. Gaining control of the interactions between vesicles of different populations will enable vesicles with different chemical contents to be brought together into higher order structures for manipulation: potentially their cargo could be mixed in small volumes by inducing fusion events between the vesicles in such conglomerates. We use single-stranded DNA (ssDNA) anchored to the vesicle membrane to bind to vesicles of a second population with the complementary ssDNA anchored to their membranes. The vesicles self-assemble into superstructures of bound vesicles directed by the specificity of the interaction between complementary ssDNA strands. We find three regimes of aggregation behaviour: no aggregation, stable aggregates and aggregates that grow until flocculates are visible in solution. The rate of aggregation is determined by the vesicle collision rate and the probability of hybridisation of complementary ssDNA strands during a collision. Vesicle binding is found to be reversible by heating above a melting temperature for the DNA duplex. The thermal stability of the DNA duplex is found to be greatly enhanced when anchored to the vesicles compared with the stability in free solution. This is caused by the enhanced local concentration and reduced conformational entropy of the DNA due to being anchored to the lipid vesicles.