It really depends on what occurs after he brings you to these family events. Does he continue to talk to you about his family members and what they are like? Or, does he barely talk about his family, if at all, until the next family event he takes you to?
If he is continuously talking to you about his family members after having taken you to these family events, he is trying to make you more acquainted with them in the hopes that you start building relationships with them. This is often a way he is able to get some insight into how you would get along with them long term.
This shows that he is thinking about taking his relationship with you more seriously.
If he barely talks about his family after having taken you to these family events, you are just someone he brings along so that he doesn’t look like the odd one out. This approach doesn’t bode well when it comes to how serious he intends to get with you in terms of your relationship.