We demonstrate that a future high-energy electron-proton collider like THERA could largely extend the current HERA program in jet photoproduction of testing QCD and determining the partonic structure of the proton and the photon. Depending on the electron beam energy (250-500 GeV) and the collider mode (ep or γp), the range in the hard transverse energy scale of the jets could be increased by a factor of 2-3 and the reach in the momentum fraction x of the partons in the proton or photon by at least one order of magnitude. It would thus become possible to check the determinations of the gluon density in the proton obtained in deep-inelastic scattering experiments, to measure the gluon density in the photon down to low values of x, and to study the QCD dynamics in multi-jet events.