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The harvest of exoplanet discoveries has opened the area of exoplanetcharacterisation. But this cannot be achieved without a careful analysis of thehost star parameters. The system of HD219134 hosts two transiting exoplanetsand at least two additional non-transiting exoplanets. We used the VEGA/CHARAinterferometer to measure the angular diameter of HD219134, leading to astellar radius of $R_{\star}=0.726\pm0.014 R_{\odot}$. We also derived thestellar density from the transits light curves ($\rho_{\star}=1.82\pm0.19\rho_{\odot}$), which finally gives a direct estimate of the mass($M_{\star}=0.696\pm0.078 M_{\odot}$) with a correlation of 0.46 between$R_{\star}$ and $M_{\star}$. This new mass is smaller than that derived fromthe C2kSMO stellar evolutionary model, which provides a mass range of0.755$-$0.810 ($\pm 0.040$) $M_{\odot}$. This allows us to infer the mass,radius and density of the two transiting exoplanets of the system. We then usean inference model to obtain the internal parameters of these two transitingexoplanets. Moreover, we find that planet $b$ and $c$ have smaller radii thanpreviously estimated ($1.500\pm0.057$ and $1.415\pm0.049 R_{\oplus}$,respectively); this clearly puts these planets out of the gap in theexoplanetary radii distribution and validates their super-Earth nature. Planet$b$ is more massive than planet $c$, but possibly less dense. We investigatewhether this could be caused by partial melting of the mantle and find thattidal heating due to non-zero eccentricity of planet $b$ may be powerfulenough. The system of HD219134 constitutes a very valuable benchmark for bothstellar physics and exoplanetary science. The direct determination of thestellar density, radius and mass should be more extensively applied to provideaccurate exoplanets properties and calibrate stellar models.

From the stellar properties of HD219134 to the internal compositions of its transiting exoplanets