Hybrid polymer/lipid vesicles are self-assembled structures that have been the subject of an increasing number of studies in recent years. They are particularly promising tools in the development of cell membrane models as they offer the possibility to fine-tune their membrane structure by adjusting the distribution of components (presence or absence of “raft like” lipid domains) which is of prime importance to control their membrane properties. Line tension in multiphase membranes is known to be a key parameter on membrane structuration but remains unexplored, either experimentally or by computer modelling for hybrid polymer /lipid vesicles. In this study we were able to measure the line tension on different budded hybrid vesicles, using micropipette aspiration technique, and show the influence of the molar mass and the architecture of block copolymers on line tension and its consequences for membrane structuration.