Abstract: The KamLAND and Borexino experiments have detected electron antineutrinos produced in the decay chains of natural thorium and uranium (Th and U geoneutrinos). We analyze the energy spectra of current geoneutrino data in combination with solar and long-baseline reactor neutrino data, with marginalized three-neutrino oscillation parameters. We consider the case with unconstrained Th and U event rates in KamLAND and Borexino, as well as cases with fewer degrees of freedom, as obtained by successively assuming for both experiments a common Th/U ratio, a common scaling of Th + U event rates, and a chondritic Th/U value. In combination, KamLAND and Borexino can reject the null hypothesis (no geoneutrino signal) at 5 sigma. Interesting bounds or indications emerge on the Th + U geoneutrino rates and on the Th/U ratio, in broad agreement with typical Earth model expectations. Conversely, the results disfavor the hypothesis of a georeactor in the Earth's core, if its power exceeds a few TW. The interplay of KamLAND and Borexino geoneutrino data is highlighted.