  Theoretical and experimental studies have supported that the electronic
structure of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure is described by
two-dimensional Dirac fermions. When the interlayer tunneling is coherent, the
electronic structure of the system becomes three-dimensional, and we expect the
peak structure to appear in the interlayer resistivity under magnetic fields.
We theoretically and experimentally show that the peak appears in the
interlayer resistivity at low temperatures and high magnetic fields. From the
experiment, we estimate that the magnitude of the interlayer tunneling is $t_1
\sim 1$ meV. Our result opens the door to investigating the three-dimensional
electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$.
