J.,
You need to get on the same page with your husband now. I worked with a guy who did the same thing. His daughter could do no wrong while he spoke the way he wanted to towards his stepdaughter. I know you say you are both stubborn but if your account of how your husband and his son are is accurate, you MUST stand in your son's corner. My coworker and his wife did not make it because he would not treat the girls the same and it eventually caused friction between his wife and him. It got to the point that his wife saw how it was affecting her daughter and she wasn't about to choose the way her husband and his daughter were behaving over her daughter.
I have another friend now who is working on leaving her husband because over the years, his indifference to her son from a previous relationship has grown to him treating her differently (not in a good way) as well.
I am not trying to scare you but I am trying to show you what has happened with other families because the one spouse wouldn't treat all of the children the same way and while the other spouse tried to ignore it for a while, the problem never just went away. If anything it got worse.
I highly suggest going to family counseling if you don't feel like you are getting anywhere with your husband and stepson. It isn't fair to your son and he has to know that you are still in his corner.
I hope things work out.
L.