We report four structures for the 1:1 water-ammonia mixture showing superionic behavior at high temperature with the space groups P4/nmm, Ima2, Pma2, and Pm, which have been identified from evolutionary random structure search calculations at 0 K. Analyzing the respective pair distribution functions and diffusive properties the superionic phase is found to be stable in a temperature range between 1000 and 6000 K for pressures up to 800 GPa. We propose a high-pressure phase diagram of the water-ammonia mixture for the first time and compare the self-diffusion coefficients in the mixture to the ones found in water and ammonia. Finally, possible implications on the interior structure of the giant planets Uranus and Neptune are discussed.