Context. Composite galaxies that contain both Seyfert and starburst components may produce very high-energy (VHE; > 100 GeV) γ-ray emission at a wide range of spatial scales, from a few Schwarzschild radii of a supermassive black hole (SMBH; R = 10 pc for M = 10 to dimensions of kiloparsec-size jet-driven outflows. In addition to supernova remnants, various sources have been suggested to explain data collected on composite galaxies, including multi-messenger neutrino and ultra-high-energy cosmic-ray data. Aims. The closest composite Seyfert–starburst galaxies (NGC 1068, the Circinus galaxy, and NGC 4945) are observed with the High Energy Stereoscopic System (H.E.S.S.) to provide constraints on cosmic-ray populations in these systems. Methods. Data obtained in H.E.S.S. observations have been analyzed to search for VHE γ-ray counterparts to the GeV γ-ray signals detected with Fermi-LAT and for potential spectral components in the VHE range. Results. No significant signals have been found in these H.E.S.S. data. Upper limits on the VHE γ-ray fluxes were applied to constrain theoretical models involving different spectral components.