Context. The study of nonthermal processes such as synchrotron emission, inverse Compton scattering, bremsstrahlung, and pion production is crucial to understanding the properties of the Galactic cosmic-ray population, to shed light on their origin and confinement mechanisms, and to assess the significance of exotic signals possibly associated to new physics. Aims. We present a public code called HERMES which is designed generate sky maps associated to a variety of multi-messenger and multi-wavelength radiative processes, spanning from the radio domain all the way up to high-energy gamma-ray and neutrino production. Methods. We describe the physical processes under consideration, the code concept and structure, and the user interface, with particular focus on the python-based interactive mode. In particular, present the modular and flexible design that allows the user to easily extend the numerical package according to their needs. Results. In order to demonstrate the capabilities of the code, we describe the details of a comprehensive set of sky maps and spectra associated to all physical processes included in the code. We comment in particular on the radio, gamma-ray, and neutrino maps, and mention the possibility of studying signals stemming from dark matter annihilation. Conclusions. HERMES can be successfully applied to constrain the properties of the Galactic cosmic-ray population, improve our understanding of the diffuse Galactic radio, gamma-ray, and neutrino emission, and search for signals associated to particle dark matter annihilation or decay.