We aim to explain in a unified way the experimental data on ultrahigh-energy cosmic rays (UHECRs) and neutrinos, using a single source class and obeying limits on the extragalactic diffuse gamma-ray background. If UHECRs only interact hadronically with gas around their sources, the resulting diffuse cosmic-ray (CR) flux can be matched well to the observed one, providing at the same time large neutrino fluxes. Since the required fraction of heavy nuclei is, however, rather large, the maxima of air showers in the Earth’s atmosphere induced by UHECRs with energies E≳3×1018  eV would be too high. Therefore, additional photohadronic interactions of UHECRs close to the accelerator have to be present, in order to modify the nuclear composition of CRs in a relatively narrow energy interval. We thus include both photon and gas backgrounds and combine the resulting CR spectra with the high-energy part of the Galactic CR fluxes predicted by the escape model. As result, we find a good description of experimental data on the total CR flux, the mean shower maximum depth Xmax and its width rms(Xmax) in the whole energy range above E≃1017  eV. The predicted high-energy neutrino flux matches IceCube measurements, while the contribution to the extragalactic diffuse gamma ray background is of order 30%.