The temperature- and magnetic-field-dependent resistivity of La0.7Ca0.3MnO3/LaNiO3 superlattices grown on (001)-oriented SrTiO3 and LaAlO3 substrates is compared as a function of LaNiO3 spacer layer thickness. The electron transport in superlattices with the spacer layer thickness ≤4 unit cells is characterized by a thermally activated resistivity p(T) between 4.2 and 300 K, and a large (∼90%) magnetoresistance at low temperatures. A parallel resistor model, which explicitly takes into account the interfacial disorder in each unit of the superlattice, correctly reproduces the broad features of the p(T) curves. We attribute the disordered interfaces to lattice-mismatch-induced strain and a magnetic roughness, which results from truncation of the three-dimensional coordination of magnetic ions at the interfaces.