Based upon the information you have provided, Jewish law would obligate the passenger for payment of the damages incurred by this accident. This is based upon the concept of aish or fire. The Mishnah says one who lights a fire which burns even a distant object must pay for the damages. The early commentaries (Tosafos Bava Kama 56a) prove from a statement of the Talmud, that when it comes to damaging someone’s property by fire there is no difference between causing the fire to spread to another’s property or moving the property into the path of the fire. Here, too, putting the door in the path of a moving vehicle is equivalent to causing the vehicle to drive into the door, similar to putting an object of another in the path of approaching fire.
As the oncoming car was also damaged, the liability of the passenger to pay for those damages as well, according to Jewish law, depends upon what caused the door to remain open at the time the car struck it. If the passenger was holding the door open, he is liable for the damages to the second car. If, however, the door was holding itself open (even though it was the passenger who originally opened it), the passenger is exempt from those damages, due to the principle of gerama benizikin or causative damages. These types of damages cannot be claimed in a court, but are “liable in the Heavenly court,” and would therefore be advised by the court to pay, but not obligated.
There are, however, other factors that could affect this ruling. If you told the passenger to open the door, he would be exempt. If the driver of the oncoming car could easily have stopped or avoided hitting the door, the passenger is also exempt, although he acted irresponsibly by opening the door (In that case, the oncoming car would not be considered like fire, which is apt to damage by putting the door in its path).
Since there are mitigating factors involved, you and the passenger should together approach an authority in Jewish monetary law to receive a final ruling.
Rabbi Yerachmiel Fried