Nicotine is a very compelling addiction, and addictions are hard to break. The user has to completely want to drop the habit, and even at that, most smokers have to try several times before they (might) finally succeed.
Your husband may well be lying to you in this one particular area because you are so insistent that he break this habit, and he wants to tell you what you want to hear. He probably wishes it were so, also.
If you can scale back the pressure, judgment, nagging, worrying out loud, whatever form your conversations take around the subject of smoking, you'll actually be removing one of his reasons to smoke. No, he probably doesn't smoke to make you upset, but to deal with pressure and feel better. Pressure from others, pressure from work, from bills, from worry, etc, all make it much more difficult to resist any addiction that might bring relief, however temporarily.
What if you were to just let him know you recognize how difficult it must be to have a habit that's so hard to break? You'll give him a chance to decide for himself whether he wants to quit.
Let him know that you'll gladly support him in any way that he asks, but that the choice is ultimately his. He already knows it's important to you, but it has to be as important to him for his own reasons. That's really the only way he's likely to succeed. In the meantime, be grateful that he does his smoking outside. You could ask him to change clothes when he comes home reeking, because even those deposits can have health consequences for your daughter and you.
Good luck. This is a hard one.