Both phospholipid vesicles and their more stable and versatile block-copolymer synthetic analogs have captured significant attention in recent years for their use in fundamental membrane studies and for their potential use in biomimetic and engineering applications. By taking advantage of biological molecular tethers (e.g., DNA hybridization or receptor-ligand interactions) vesicles can be systematically docked together to create novel super-structures. In this study, we create hybrid structures conjoining phospholipid and diblock copolymer (Polybutadiene-Polyethyleneoxide) vesicles. The vesicle membranes are decorated such that they present biotin or single-stranded DNA or both. Spacer groups (PEG) can be coupled to these adhesive moieties allowing control of their position relative to the hydrophobic core of the membrane. The impact of surface chemistry on vesicle binding and adhesion plague growth at the contacting interface is demonstrated by a dual micropipette manipulation technique and confocal microscopy. The binding strengths at the interface between vesicles (polymersome, liposome or their hybrid) are determined by the location of the adhesive molecules relative to the membrane's brush architecture. Fastest adhesion kinetics are observed when the adhesive moieties are positioned outside hydrophilic corona of the block copolymers. Binding is not observed when the adhesive moieties are buried within the hydrophobic brush due to the inaccessibility and steric hindrance of brush layer. Superstructures of phospholipid vesicles tethered by biotin-avidin interactions are seen to degrade after several days whereas polymersomes bound by these specific bonds are much more stable. Hybrid block-copolymer/phospholipid vesicles show better mechanical stability than pure phospholipid vesicles whilst binding of these hybrids is also possible using the membrane-anchored DNA: something that is not possible with pure block-copolymer vesicles due to its longer hydrophilic brush layer. Therefore, these block-copolymer/phospholipid hybrid vesicles exhibit the advantageous properties of each of the individual polymersome and liposome systems. By controlling the binding strength and membrane properties of these programmable, hierarchical assemblies and the technological utilities of polymeric and phospholipids vesicles, these self-assembled superstructures could be applied as a versatile platform for biotechnologies and new delivery techniques.