Liquid interfaces and membranes represent two physically opposite regimes of interfacial dynamics: the former are governed by interfacial tension, while the latter are governed by bending elasticity. What happens when these two extremes are combined by confining a coacervate liquid within a membrane geometry is a largely unexplored question. Here, we probe the membrane dynamics of polyelectrolyte complex vesicles with coacervate cores using neutron spin echo spectroscopy. The relaxation rate follows Γ ~ q3 (where q denotes the magnitude of the scattering vector), demonstrating that bending undulations prevail despite the intrinsically liquid nature of the constituents. However, the reduced relaxation rate is more than an order of magnitude higher than that of lipid bilayers, despite the four-fold larger membrane thickness, indicating an exceptionally weak bending restoring force. The reduced relaxation rate η0Γ/kBT (where η0 and kBT denote the solvent viscosity and thermal energy, respectively) remains invariant across temperatures and salt concentrations, indicating that the bending elasticity is entropic in origin. Thus, the geometric constraint of the vesicular structure imposes bending-undulation dynamics on an otherwise liquid interface while preserving the entropy-driven nature of the coacervate.