The rotational motions of the internal Earth layers induce resonances in the Earth nutations and tidal gravimetric response to external luni-solar gravitational forcings. The characterization of these resonances is a mean of investigating the deep Earth properties since their amplitudes and frequencies depend on a few fundamental geophysical parameters. In this work, we focus on the determination of the free core nutation and free inner core nutation periods and quality factors from the Bayesian inversion of VLBI and gravimetric data. We make a joint inversion of data from both techniques and show that, even if the results are only slightly different from the inversion of VLBI data alone, such approach may be valuable in the future if the accuracy of gravimetric data increases. We also briefly discuss the polar motion resonance, which is related to the Chandler Wobble as seen from the diurnal frequency band. Our overall estimates of the FCN period and quality factor, T FCN = (−430.2, −429.8) solar days and Q FCN = (15 700, 16 700), respectively, are in good agreement with other studies, albeit slightly different for unclear reasons. Despite some concerns about the detection and characterization of the FICN, it seems that we could also successfully estimate its period, T FICN = (+600, +1300) solar days, and give a loose estimate of the upper bound on its quality factor.