Cosmic rays (CRs) interact with the diffuse gas, radiation, and magnetic fields in the interstellar medium (ISM) to produce electromagnetic emissions that are a significant component of the all-sky flux across a broad wavelength range. The Fermi–Large Area Telescope (LAT) has measured these emissions at GeV γ-ray energies with high statistics. Meanwhile, the high-energy stereoscopic system (H.E.S.S.) telescope array has observed large-scale Galactic diffuse emission in the TeV γ-ray energy range. The emissions observed at GeV and TeV energies are connected by the common origin of the CR particles injected by the sources, but the energy dependence of the mixture from the general ISM (true ‘diffuse’), those emanating from the relatively nearby interstellar space about the sources, and the sources themselves, is not well understood. In this paper, we investigate predictions of the broad-band emissions using the galprop code over a grid of steady-state 3D models that include variations over CR sources, and other ISM target distributions. We compare, in particular, the model predictions in the very-high energy ( VHE; ≳100 GeV) γ-ray range with the H.E.S.S. Galactic plane survey (HGPS) after carefully subtracting emission from catalogued γ-ray sources. Accounting for the unresolved source contribution, and the systematic uncertainty of the HGPS, we find that the galprop model predictions agree with lower estimates for the HGPS source-subtracted diffuse flux. We discuss the implications of the modelling results for interpretation of data from the next generation Cherenkov Telescope Array (CTA).