For a parallel-plane barrier heterostructure of any form or composition, it is shown by considering the electron quantum states as functions of complex values of the energy that the full linewidth of a resonant peak in the coherent transmission probability, 2 \ensuremath{\Delta}E, and the tunneling lifetime of the quasilevel giving rise to the resonance, \ensuremath{\tau}, are necessarily related by (2 \ensuremath{\Delta}E)\ensuremath{\tau}=\ensuremath{\Elzxh}, and the conventional wave-packet transit time is 2\ensuremath{\tau} at the resonance energy. A formula is obtained for the peak transmission probability in terms of the ratio of the two outward currents for an electron escaping from the quasilevel.