Context.The number of exoplanets with precise mass and radius measurements is constantly increasing thanks to novel ground- and space-based facilities such as HARPS, ESPRESSO, CHEOPS, and TESS. The accuracy and robustness of the planetary characterization largely depends on the quality of the data, but also requires a planetary structure model, capable of accurately modeling the interior and atmospheres of exoplanets over a large range of boundary conditions.Aims.Our goal is to provide an improved characterization model for planets with masses between 0.5 and 30 Earth masses, equilibrium temperatures below <2000 K, and a wide range of planetary compositions and physical phases.Methods.In this work, we present the Bayesian Interior Characterization of ExoPlanetS (BICEPS) model, which combines an adaptive Markov chain Monte Carlo sampling method with a state-of-the-art planetary structure model. BICEPS incorporates many recently developed equations of state suited for large ranges of pressures and temperatures, a description for solid and molten planetary cores and mantles, a gaseous envelope composed of hydrogen, helium, and water (with compositional gradients), and a non-gray atmospheric model.Results.We find that the usage of updated equations of state has a significant impact on the interior structure prediction. The impact varies, depending on the planetary composition. For dense rocky planets, BICEPS predicts radii a few percent different to prior internal structure models. For volatile rich planets, we find differences of 10% or even larger. When applying BICEPS to a particular exoplanet, TOI-130 b, we inferred a 25% larger water mass fraction and a 15% smaller core than previous models.Conclusions.The presented exoplanet characterization model is a robust method applicable over a large range of planetary masses, compositions, and thermal boundary conditions. We show the importance of implementing state-of-the-art equations of state for the encountered thermodynamic conditions of exoplanets. Hence, using BICEPS improves the predictive strength of the characterization process compared to previous methods.