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We present a self-consistent prediction of the interstellar radiation field (ISRF), from the extreme ultraviolet (EUV) to sub-mm range, based on two chemical evolution models of a Milky Way-like galaxy (MWG). To this end, we develop a new tool called Mixclask to include gas emission, absorption and scattering from the photoionization code Cloudy into the Monte Carlo radiative transfer code Skirt. Both algorithms are invoked iteratively, until the physical properties of the ISM converge. We have designed a first test, reminiscent of a HII region, and we find that the results of Mixclask are in good agreement with a spherically symmetric Cloudy simulation. Both MWG models based on chemical evolution codes give results broadly consistent with previous empirical models reported in the literature for the ISRF of our Galaxy, albeit they systematically underestimate the mid-infrared emission. We also find significant differences between our two models in the whole ultraviolet range, not fully explored in previous ISRF models. These results show the feasibility of our method of combining radiative transfer with chemical evolution models: there is increased predictive power and the interstellar radiation field obtained provides further constraints on the model parameters. Python source code to implement our method is publicly available at https://github.com/MarioRomeroC/Mixclask.