We definitely don't "require" check-ins from each other - we're both adults, after all. But as a courtesy, I'll check in if I'm going to be out later than I thought, or even if I just need to hear a friendly voice.
I think if you're having some serious issues with trust or anything else, some good solid communication can't hurt. In fact you may be able to figure out exactly why he's expecting you to check in, because there has to be something behind it - and there's no need to assume (without proof) that it's a negative feeling behind his desire for the check-ins. (like lack of trust, for example)
A communication technique we've started using this past year is called "mirroring". If you do an internet search for "Imago Mirroring Dialogue" you can even find a website where you can sign up for a free 12 week course that will be sent to your email each week. It walks you through the basic mirroring dialogues, and helps you learn how to use this tool as a couple to avoid arguments and tensions.
What we like about it is that there is an actual prescribed dialogue to follow. With practice, it has allowed us to create a "neutral zone" in which each of us is free to express concerns, fears, worries, etc. without making the other person feel attacked. It allows each of us to listen to the other without feeling defensive, and just hear them and what they need.
It's been a wonderful process for us, and I think it really might help you and your husband too. Especially after 10 years and 2 kids, that sounds like something worth saving - and if it's worth saving it's also worth improving in my book! Best wishes to you both!