Wow, you have brought me back 24 years. You are going through exactly what I went through in the beginning of my marriage. My husband had two children when I met him, a son who was 3 and a daughter who was 3 months at the time. Although I didn't take his children in until I had my own daughter, they did move in with us when they were 10 and 7. Not an easy thing to do, but I am sure you are like I was, you married a package deal and you stand by it. But..... and I do mean BUT!!! You need to take "yourself" into consideration. You are not happy. You are being taken advantage of. Why weren't either parent at that child's first day of school? There is no excuse. Kudos to you, as you realize this child has no fault and you treat him as your own. Your husband needs to start taking responsibility around the house, especially when it comes to dealing with his child and his child's mother. Step back and don't do it all. If it doesn't get done then let it be. When he complains, tell him to get his butt up and do it cause you have enough to do. If you continue to do it all, he's going to continue letting you do it all.
Well, a brief conclusion to my story. My step children and my daughter are grown now and we had another son years later who is not a teenager. After I gave all my life to this man and helped raise his children, dealt with his children's mother, took care of the house, paid the bills, and worked full time, he decided he was going to cheat on me, and did so several times, which I've recently found out. I figured the kids are now grown, now we can do all the things we never had a chance to do because we were busy raising a family.
This doesn't mean that this is what will happen to you, I just want to advise you not to get lost in all of this. Take good care of yourself. Love yourself and don't allow anyone to take advantage of you. You are young and you have a whole life ahead of you.
By the way, my step children keep in touch with me and have given me beautiful grandchildren. They do grow up to love you. They call me more than they call their dad. I love them just as much as I love my own.