Electron transport longitudinal to hydrogenated amorphous silicon/silicon nitride (a‐Si:H/a‐SiNx:H) multilayer structures (superlattices) with various barrier layer thicknesses has been measured by the time‐of‐flight method. The barrier thickness dependence of the electron drift velocity supports a transport model based on tunnel hopping from well to well under the influence of frequent trapping events in each well. The applied voltage dependence of the drift velocity is significantly superlinear in contrast with a linear character in bulka‐Si:H samples. The occurrence of the superlinearity is discussed by considering the applied voltage dependence of various effects which limit the longitudinal electron transport in superlattice structures. The occurrence of the superlinearity is possibly dominated by the existence of continuous distribution of deep traps in the gap of well layers rather than the applied voltage dependence of the tunneling rate, taking into account various possible effects.