Complex interfaces stabilized by proteins, polymers or nanoparticles, have a much richer dynamics than those stabilized by simple surfactants. By subjecting fluid-fluid interfaces to step extension-compression deformations, we show that in general these complex interfaces have dynamic heterogeneity in their relaxation response that is well described by a Kohlrausch-Williams-Watts function, with stretch exponent β between 0.4–0.6 for extension, and 0.6–1.0 for compression. The difference in β between expansion and compression points to an asymmetry in the dynamics. Using atomic force microscopy and simulations we prove that the dynamic heterogeneity is intimately related to interfacial structural heterogeneity and show that the dominant mode for stretched exponential relaxation is momentum transfer between bulk and interface, a mechanism which has so far largely been ignored in experimental surface rheology. We describe how its rate constant can be determined using molecular dynamics simulations. These interfaces clearly behave like disordered viscoelastic solids and need to be described substantially different from the 2d homogeneous viscoelastic fluids typically formed by simple surfactants.