We study mixtures of charged surfactants, which alone in solution form uni- and multilamellar vesicles, and oppositely charged polyelectrolytes (PEs). The phase behavior is investigated at fixed surfactant concentration as a function of the PE-to-surfactant charge ratio $x$. We find that, for $x>0$, aggregates form. Light microscopy and X-ray scattering experiments show that the isoelectric point plays a crucial role since the morphology and the microscopic structure of the aggregates are different before ($x\leq1$) and after the isoelectric point ($x>1$). To better understand the dynamics for the formation of PE/surfactant complexes, we perform light microscopy experiments where we follow in real-time the effect of a PE solution on one multilamellar vesicle (MLV). We find that the PE induces a peeling of the bilayers of the MLV one by one. The peeling is accompanied by strong shape fluctuations of the MLV and leads ultimately to a pile of small aggregates. This novel phenomenon is analyzed in detail and discussed in terms of PE-induced tension, and pore formation and growth in a surfactant bilayer.