Don't listen to people who say it's a bad idea based on type, 2XtremeENFP! If it works for you, then that's what matters...
As for how to deal with the ISTJ mom, I'm not sure I have much great advice for ISTJ people in specific. I'm trying to think if I know any ISTJs in RL (I don't know the types of most of the people I know in real life, so I don't know how to know what an ISTJ would care about for their offspring).
In general, though, I'd say just do your best to show that you're responsible and that you care for this guy and that you're not flaky or wild, at least when it comes to your relationship. In addition, trying to develop a relationship with her personally could be a good way to go. Obviously you're trying to do this and it's tough because you don't have a lot of the same tastes as the rest of the family, but certainly there must be at least SOME common interest over which you could bond... try to reach out in small ways. Maybe even try to understand why they like the things that they do...? Also, have you talked to him about it? You could tell him how you want to get to know his family/mother better, ask him does he have any suggestions? Any fun activities you can do with them and him together?
Of course, after a certain point there's only so much you can do, right? If he has made the choice to be with you, that matters more. Well, I guess how old are you guys? That could have an impact on the situation too. Sorry if you mentioned it already somewhere else in the thread.