The potential energy curves for the hydrogen-antihydrogen (HH) system in states with a leptonic orbital angular momentum projection Lambda=0, 1, 2, 6, and 30 are presented. Within the framework of the adiabatic picture, explicitly correlated Gaussians are used as basis functions which describe accurately the hydrogen-antihydrogen interaction. The critical internuclear distances where the system transforms into positronium and protonium atoms are found. Adiabatic corrections to the potential energy curves are also estimated.