Potential energy curves for excited leptonic states of the helium-antihydrogen system are calculated within the Ritz variational approach. An explicitly correlated ansatz for the leptonic wave function is employed describing accurately the motion of the leptons (two electrons and positron) in the field of the helium nucleus and of the antiproton with an arbitrary orbital angular momentum projection Lambda onto the internuclear axis. Results for Lambda=0, 1, and 30 are presented. For quasibound states with large values of Lambda and rotational quantum numbers J>Lambda no annihilation and rearrangement decay channels occur; i.e., they are metastable.