Can I get the drug charges dropped since I had no idea he had them in the car?

What you have is a defense. If they state decides not to drop your case, then you have a choice of demanding a jury trial where the state must prove that you had care, custody, and control of the drugs. Drug cases are very fact sensitive. You should speak to a local criminal defense attorney. There are rarely guarantees in anything, especially criminal law. No attorney should guarantee you a dismissal, as they do not yet have all the facts. Good luck.