I'm not sure dual diagnosis would be appropriate because his drinking and pot use may be stemming directly from his anxiety. I have severe anxiety and I know marijuana relaxes me. Several states are making note of this and approving marijuana for medicinal use. My own psychiatrist says she would strongly consider prescribing marijuana for me if it were legal in my state.
More importantly, if he is labeled an addiict, they won't give him benzodiazepines ( drugs in the Valium family) there are improved versions like: Klonopin, Xanax, and Ativan. It is my experience that these work best for anxiety. Those who are labeled addicts however are given dangerous neuroleptics instead like: Zyprexa, Risperdal, Seroquel, and Abilify. They can have life long side effects like symptoms that mimic Parkinson's disease and the rare but deadly Neuroleptic malignant syndrome. In my long experience with anxiety and depression, benzodiazepines are best.