D.B.
You don't have a stepson problem. You have a husband problem. I'm not sure why this tendency to indulge and excuse the child's laziness wasn't evident early on, but you've seen it for 11 years, so ....this is your reality.
You're right to expect chores. You're right if you think this teen is headed for tons of trouble, with teachers and employers and love interests. You're wrong to think you can make it happen or that it's your role as stepmother. I'm a stepmother, and I can tell you that I'm not the parent. My husband is. I have had many private discussions with my husband (and I saw his parenting for several years before we married) because, even with prior knowledge and discussion, things come up. It's a tough sea to navigate, even if you're mostly on the same page.
You're totally wrong to have an argument in front of a child. The only mature statement in the paragraph you wrote is your stepson saying you should find something else to argue about in front of him! Seriously, what are you thinking? Marital discord is not something to show in front of a child. So, in that sense, your husband was right to comfort his son, although wrong to participate in the argument to begin with.
Get marriage counseling. Now. What you want and need doesn't matter in your relationship. You come third in this family. The child comes second, and your husband's desire to be the Party Dad who makes everything fun and easy comes first.