If the passengers on that airplane felt their collective hearts stop for a moment, it wasn't due to the electric current from the lightning strike running through their bodies. In fact, airplanes getting struck by lightning is a fairly common occurrence -- more common than you might realize.
Because the aluminum hull of an aircraft is highly conductive, an electrically charged storm cloud will tend to induce a charge separation (or polarization) on the outer surface of any airplane in the vicinity. This creates a difference in potential -- a.k.a. voltage -- between the cloud and the plane, resulting in a discharge of electric current between them. Since there is also a potential difference between the airplane and the tarmac, the lightning discharges right through the airplane and into the ground.
But why doesn't the gigantic amount of current, which is in the neighborhood of 20,000 amps for a typical lightning bolt, harm the passengers inside the aircraft? Because the hull of the plane forms a Faraday cage! A Faraday cage is a hollow shell made of conducting material. A strong electric field outside the cage will force the charge in the material of the cage to redistribute itself, but the interior space inside the cage remains uncharged. As long as you're inside the airplane, not on its surface, it can get struck by lightning all day and you'll be fine -- physically, at least, although you may feel a bit freaked out.
What's much more dangerous for airplanes than lightning is the turbulent weather that usually accompanies an electrical storm. For the same reason, you don't get electrocuted when lightning strikes your car (provided your car is made of metal and not fiberglass, you don't have a cloth convertible roof, and you're not touching the outside surface). It's a common misconception that the insulating rubber tires protect you. Not true. It's the Faraday cage.
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.