We have similar here. I worry hugely about my DS who sleeps at the back of the house and therefore nearer all the gardens. We have neighbours everywhere out in the gardens - behind and to the left and to the right. Sometimes it's parties with music, often it's just sitting out and eating / drinking / talking. He has ASD and trouble sleeping, for which he takes medication. So far, we've managed to time it that he goes to bed when drowsy with the meds, and we keep the windows closed and don't make any mention of the noise. So far so good.
I wouldn't be able to sleep through it though and I, too, get wound up even though, most of the time, I know that these people are just enjoying the warm evenings and not meaning any harm.
I understand where your DH is coming from. Often the anticipation / anxiety / annoyance about the inconsideration of others is far worse than the actual net noise.
We have been frequently disturbed / woken up this summer by our new neighbours who seem to have the world and his wife over at the drop of a hat late at night. They're not exactly partying and there's no music but they make a fuck of a lot of racket saying goodbye to each other (right under our bedroom window). I'm trying to suck it up in the knowledge that, come the autumn, there'll be less of it. And particularly happy this week because they're on holiday!
I would suggest you keep the windows closed. We always have done. Set a fan with a timer perhaps? Ear-plugs. I'd rather be hot than bothered by noise.