The characterization of exoplanets relies on that of their host star. However, stellar evolution models cannot always be used to derive the mass and radius of individual stars, because many stellar internal parameters are poorly constrained. Here, we use the probability density functions (PDFs) of directly measured parameters to derive the joint PDF of the stellar and planetary mass and radius. Because combining the density and radius of the star is our most reliable way of determining its mass, we find that the stellar (respectively planetary) mass and radius are strongly (respectively moderately) correlated. We then use a generalized Bayesian inference analysis to characterize the possible interiors of 55 Cnc e. We quantify how our ability to constrain the interior improves by accounting for correlation. The information content of the mass-radius correlation is also compared with refractory element abundance constraints. We provide posterior distributions for all interior parameters of interest. Given all available data, we find that the radius of the gaseous envelope is $0.08 pm 0.05 R_p$. A stronger correlation between the planetary mass and radius (potentially provided by a better estimate of the transit depth) would significantly improve interior characterization and reduce drastically the uncertainty on the gas envelope properties.
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