I have to agree with Carla. In fact, you told your husband that "he is an adult and can make that decision for himself." Because you further expressed your negative feelings about the tobacco (which you have every right to do), he probably "promised" you in a well-meaning moment of remorse over his habit. That doesn't mean that he didn't regret his promise later, when feeling either social pressure or the addictive lure of the drug, and was ashamed or otherwise reluctant to tell you about backsliding.
But it is his decision, and you may well have little "secrets" about your cravings, desires and habits (spending on little splurges? a sweet tooth? clothing sales? romance novels? gossip? etc?).
And to a very large degree, it is your choice whether or not to trust him, too. One way to help with this is to be sure that lines of communication are open, with both of you able to freely express your feelings, needs, ans wishes to each other. Since you are having this discomfort, own up to it and talk to him. Do this sooner rather than later if you don't want it to become an issue that drags your relationship down. Speak in terms of YOUR feelings and YOUR needs, not what he does or your suspicions about him. Be sure he hears from you clearly that it's much more important to you that you hear the truth than some story that he thinks will make you happy.
Consider that if he's messing around in ways detrimental to your relationship, evidence will begin to surface. You won't have to go looking for it. It's possible that the bank story will soon be followed by other events, and there will be changes in his attitude and availability that that you can't ignore.
And if he's NOT messing around, the bank story will probably check out (if you want evidence one way or another, look for a deposit or withdrawal on your statement).
Suspicion is in itself terribly detrimental to the health and longevity of a relationship. A partner under constant suspicion will begin to hide behaviors, preferences and habits, rather than have to explain them.