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(abridged) Spectroscopic observations of high-redshift galaxies slowly reveal the same complexity of the interstellar medium (ISM) as expected from resolved observations in nearby galaxies. While providing a wealth of diagnostics, such high-z spectra are often unresolved, and inferring reliable diagnostics represents a major obstacle. Bright, nearby, unresolved galaxies provide many constraints to design methods to infer ISM properties, but they have so far been limited to deterministic methods and/or with simple topological assumptions. Multicomponent ISM models associate a complex enough distribution of matter and phases with a simple enough topological description to be constrained with probabilistic frameworks. Our goal is to provide a flexible statistical framework that is agnostic to the model grid and that considers either a few discrete components defined by their parameter values and/or statistical distributions of parameters. In this study we present a the MULTIGRIS framework and use it to model a suite of spectral lines in the star-forming regions of the metal-poor dwarf galaxy IZw18. We are able to calculate accurate values for the metallicity, number of ionizing photons, masses of ionized and neutral hydrogen, as well as the dust mass and the dust-to-gas mass ratio. We find a relatively modest amount of H$_2$ which is predominantly CO-dark and traced by C$^+$ rather than C$^0$. Nevertheless, more than $90$% of the [CII] emission is associated with the neutral atomic gas. Our models confirm the necessity to consider an X-ray source. Finally, we investigate the escape fraction of ionizing photons for different energy ranges. While the escape fraction for the main HII region lies around $50-65$%, we show that most of the soft X-ray photons are able to escape and may play a role in the ionization and heating of the circumgalactic or intergalactic medium.