Of course the drug tests are wrong! Oh If I had a nickel for every time I heard someone say that. "Those tests are worthless...all false positives, etc etc.
The fact is you busted him, he knows it, and he's pissed. You caught him lying, which makes him feel like crap because no one wants to be told they're a liar. But the post above me by zoso is right. Make your plan. Give him the ultimatum and stick to it. If he decides not to seek help, then leave. You have too much on your plate to be hobbled by a coke addict/alcoholic. Keep right here on SR. I wish you well.