Sounds like things are out of balance for you. You can talk about that without nagging. Present it as a puzzle for the two of you to solve, and be clear in your own head about what the desired outcome is. Do you want him home more often so that you can all spend time together? Or do you want him home more often so that he can spend time with the kids and you can do what you want (go out, read a book, do chores in peace)?
I work 3 days a week at home, 2 in the office, teach SAT prep, and am on a PTA board. I also go to meetings for things like the hockey boosters and try to socialize with different groups of friends once a month each (so maybe 1-3 get-togethers a month). Add in going to the gym or training for a race and there are times when it seems like I'm never at home. We have teenagers who can watch the younger kids so sometimes my husband isn't home either. However, I do get the kids off to school every day, I'm the one with the flexibility to bring them somewhere after school (friend's house, soccer practice), I teach Sunday school for them and bring them to church, I arrange their play dates, know their friends, bring them to birthday parties, get to most sporting events, and plan most meals even though I'm not home to cook or eat many of them. I did drop out of the garden club and a book club because it was just too much, but my husband definitely resents that I go out a lot.
On the other hand, he's not a social guy or a joiner so he doesn't go out much by choice. He does play hockey once a week or so, which is great, and sometimes goes to the gym, which is also great, but he'd rather be home, so to me, that looks like "yes I can go to that meeting" or "sure, I can do a tutoring session on Tuesday night" because I feel no need for us to both be home. We "divide and conquer" instead of spending every day as a family at home. That's partly a function of our dysfunctional marriage (we don't like each other a lot of the time) and partly out of the need to get 4 kids different places - I can pick one up from soccer at 6:30, go to a PTA meeting, drop another off at a late hockey practice, go to the gym, pick up from practice at 10 and be home at 10:15.
If he's an extrovert, he might be thinking that because you've got things covered at home, there's no need for you to both be there all the time. That's not working for you, so let him know what you perceive to be the problem, what a solution looks like to you, and let him come up with steps that he can take to get there.