We report a comprehensive formalism for the electrokinetics (streaming current, I _str) at soft multilayered polyelectrolyte films. These assemblies generally consist of a succession of permeable diffuse layers that differ in charge density, thickness, and hydrodynamic softness. The model, which extends one that we recently reported for the electrokinetics of monolayered soft thin films (Langmuir 2010, 26, 18169-18181), is valid without any restriction in the number and thickness of layers, or in the degree of dissociation and density of ionizable groups they carry. It further covers the limiting cases of hard and free draining films and correctly compares to semianalytical expressions derived for I _str under conditions where the Debye-Hückel approximation applies. The flexibility of the theory is illustrated by simulations of I _str for a two-layer assembly of cationic and anionic polymers over a large range of pH values and electrolyte concentrations. On this basis, it is shown that the point of zero streaming current (PZSC) of soft multilayered interphases, defined by the pH value where I _str = 0, generally depends on the concentration of the (indifferent) electrolyte. The magnitude and direction of the shift in PZSC with varying salinity are intrinsically governed by the dissymmetry in protolytic characteristics and density of dissociable groups within each layer constituting the film, together with the respective film thickness and hydrodynamic softness. The fundamental effects covered by the theory are illustrated by streaming current measurements performed on two practically relevant systems, a polyelectrolyte bilayer prepared from poly(ethylene imine) (PEI) and poly(acrylic acid) (PAA) and a polymer-cushioned (PEI) bilayer lipid membrane.