This is an interesting one. I used to smoke pot and drink at the same time. Both, every day, for years. Then, one day, I moved away from my pot smoking friends, and I just quit - cold turkey. The alcohol was a different story.
With the pot, you don't get the physical withdrawal symptoms. Cravings, sure, but I at least didn't have any shakiness, nausea, sweats, like I get from alcohol withdrawal. However I know friends who cannot for the life of them go a day without a smoke.
I'd say go talk to an addiction specialist and be totally truthful with them.