You need to talk to your husband, point out the inequities in his parenting decisions, and then point out how his son is affecting your family.
You need to put your foot down at some point. We've had to do this with our daughter who acted similarly - lying, stealing, wouldn't get a job, out all hours, etc... - and ended up at the decision that she is no longer welcome to live in our home. We have a 14 year old at home and a new baby on the way, and the welfare and sanity of those two children is just more important than a "young adult" who won't change and doesn't show any signs of wanting to do so.
Talk to your husband and be firm. Come up with a plan regarding your step-son and agree to stick to it. Something like 'must have a job by X', rules he must live by in the house, how he can contribute to the house, etc...whatever makes sense for (1) teaching him responsibility and (2) taking some of the stress out of your home.
I know it's hard, having been through a similar situation recently, but in the end it's better not only for the rest of your family but for your step-son. Sometimes tough love is the only answer and some children have to hit "rock bottom" before they can figure out they need to be responsible for themselves.
By setting some goals/rules it will help to alleviate any guilt you might feel when he doesn't fulfill his obligations or meet goals. You can't - or shouldn't - support him forever. He's technically an adult, it's time he grew up and acted like one.