Epitaxial BaTiO3 films and epitaxial BaTiO3/SrTiO3 multilayers were grown by pulsed laser deposition on vicinal surfaces of (001)-oriented Nb-doped SrTiO3 (SrTiO3:Nb) single-crystal substrates. Atomic force microscopy was used to investigate the surface topography of the deposited films. The morphology of the films, of the BaTiO3/SrTiO3 interfaces, and of the column boundaries was investigated by cross-sectional high-resolution transmission electron microscopy. Measurements of the dielectric properties were performed by comparing BaTiO3 films and BaTiO3/SrTiO3 multilayers of different numbers of individual layers, but equal overall thickness. The dielectric loss saturates for a thickness above 300 nm and linearly decreases with decreasing film thickness below a thickness of 75 nm. At the same thickness of 75 nm, the thickness dependence of the dielectric constant also exhibits a change in the linear slope both for BaTiO3 films and BaTiO3/SrTiO3 multilayers. This behaviour is explained by the change observed in the grain morphology at a thickness of 75 nm. For the thickness dependence of the dielectric constant, two phenomenological models are considered, viz. a 'series-capacitor' model and a 'dead-layer' model.