Context. High-energy emission of extragalactic objects is known to take place in relativistic jets, but the nature, the location, and the emission processes of the emitting particles are still unknown. One of the models proposed to explain the formation of relativistic ejections and their associated non-thermal emission is the two-flow model, where the jets are supposed to be composed of two different flows, a mildly relativistic baryonic jet surrounding a fast, relativistically moving electron positron plasma. Here we present the simulation of the emission of such a structure taking into account the main sources of photons that are present in active galactic nuclei (AGNs).Aims. We try to reproduce the broadband spectra of radio-loud AGNs with a detailed model of emission taking into account synchrotron and inverse-Compton emission by a relativistically moving beam of electron positron, heated by a surrounding turbulent baryonic jet.Methods. We compute the density and energy distribution of a relativistic pair plasma all along a jet, taking into account the synchrotron and inverse-Compton process on the various photon sources present in the core of the AGN, as well as the pair creation and annihilation processes. We use semi-analytical approximations to quickly compute the inverse-Compton process on a thermal photon distribution with any anisotropic angular distribution. The anisotropy of the photon field is also responsible for the bulk acceleration of the pair plasma through the “Compton rocket” effect, thus imposing the plasma velocity along the jet. As an example, the simulated emerging spectrum is compared to the broadband emission of 3C 273.Results. In the case of 3C 273, we obtain an excellent fit of the average broadband energy distribution by assuming physical parameters compatible with known estimates. The asymptotic bulk Lorentz factor is lower than what is observed by superluminal motion, but the discrepancy could be solved by assuming different acceleration profiles along the jet.Key words: galaxies: active / radiation mechanisms: non-thermal / gamma rays: general / quasars: individual: 3C 273 / galaxies: jets