Context. Interpretation of the X-ray spectra of X-ray binaries during their hard states requires a hot, optically thin medium. There are several accretion disc models that account for this aspect. However, none is designed to simultaneously explain powerful jets detected during these states. Aims. A new quasi-Keplerian hot accretion disc solution, a jet emitting disc (JED hereafter), which is part of a global disc-jet MHD structure producing stationary super-alfvénic ejection, is investigated here. Its radiative and energetic properties are then compared to the observational constraints found in Cygnus X-1. Methods. We solve the disc energy equation by balancing the local heating term with advection and cooling by synchrotron, bremsstrahlung, and Comptonization processes. The heating term, disc density, accretion velocity, and magnetic field amplitude were taken from published self-similar models of accretion-ejection structures. Both optically thin and thick regimes are considered in a one-temperature, gas-supported disc. Results. Three branches of solutions are found to be possible at a given radius, but we only investigate the hot, optically thin and geometrically slim solutions. These solutions give simultaneously and consistently the radiative and energetics properties of the discjet system. They are able to reproduce the global accretion-ejection properties of Cygnus X-1 very well, namely its X-ray spectral emission, jet power, and jet velocity. About half of the released accretion power is used to produce two mildly relativistic (v/c 0.5) jets, and for a luminosity of about 1% of the Eddington luminosity, the JED temperature and optical depth are close to what is observed in the hard state of Cygnus X-1. Conclusions. The accretion and ejection properties of JEDs agree with the observations of the prototypical black hole binary Cygnus X-1. The JED solutions are likely to be relevant to the whole class of microquasars.