Context. Local metal-poor galaxies stand as ideal laboratories to probe the properties of the interstellar medium (ISM) in chemically unevolved conditions. Detailed studies of this primitive ISM can help gain insights on the physics of the first primordial galaxies that may be responsible for the Reionization. Quantifying the ISM porosity to ionizing photons in nearby galaxies may improve our understanding of the mechanisms leading to Lyman Continuum photons leakage from galaxies. The wealth of infrared (IR) tracers available in local galaxies and arising from different ISM phases allows us to constrain complex models in order to estimate physical quantities. Aims. Primitive galaxies with low metal and dust content have been shown to host a more patchy and porous ISM than their highmetallicity counterparts, with numerous density-bounded regions from where ionizing photons might leak out. To what extent this peculiar structure contributes to the leakage of ionizing photons remains to be quantitatively studied. Such effects can only be investigated by accounting for the complexity and inhomogeneity of the ISM. We aim to provide a new statistical framework to quantify various galactic observables by constraining a representative multi-phase and multi-sector topology using a combination of 1D models. Methods. To address these questions we build a refined grid of models including density-bounded regions and a possible contribution of an X-ray source. Using MULTIGRIS, a new Bayesian code based on Monte Carlo sampling, we combine the models as sectors under various assumptions to extract the probability density distributions of the parameters and infer the corresponding escape fractions from H ii regions ( f esc,HII ). We apply this new code to a sample of 39 well-know local starbursting dwarf galaxies from the Dwarf Galaxy Survey (Madden et al. 2013). Results. We confirm previous results hinting at an increased porosity to ionizing photons of the ISM in low-metallicity galaxies and provide, for the first time, quantitative predictions for f esc,HII . The predicted f esc,HII for low-metallicity objects span a large range of values, up to ∼60%, while the values derived for more metal-rich galaxies are globally lower. We also examine the influence of other parameters on the escape fractions, and find that the specific star-formation rate correlates best with f esc,HII . Finally, we provide observational line ratios which could be used as tracers of the photons escaping from density-bounded regions. Among other, we discuss the possible caveats of diagnostics based on [C ii]158µm in low-metallicity environments as we find a strong metallicity dependency of the fraction of [C ii]158µm emitted in the different ISM phases. Conclusions. The new framework presented in this paper allows us to use suites of unresolved IR emission lines to constrain various galactic parameters, including the escape fraction of ionizing photons from H ii regions. Although this multi-sector modelling remains too simple to fully capture the ISM comple...