Going against the grain here.
It's really nice of you, but I think if it was me, I would say no.
I have family, (close and extended,) who I socialise with a few times a year, and also work colleagues who I go out with every 3-4 months, and also 3 good friends who I have known since childhood, who I go out with for a night out about once a month. Then me and DH go out in between. So I don't need any more friends or people in my life to 'do stuff' with. So I wouldn't want to muddy the waters by accepting a neighbour invitation, not even at Christmas. (I am sure someone will slag me off for saying that, and call me a miserable cow, but I am entitled to feel this way.)
My neighbours are pleasant, and we chat over the fence for 10 minutes once or twice a week during summer, and clear and salt each others drives in the snow and ice, and would be there in a emergency. But that is where it ends. I have no wish to socialise with them.
One couple asked me and DH around about 5 years ago, about 6 months after we moved in, and although they were pleasant, we felt quite awkward and stuck for what to say. We stayed an hour an a half and then left. We never asked them in return, and they never asked us again.
We still got on ok, and I think after that one time, they realised we felt a bit uneasy in someone else's house. They actually moved house 2 years after we moved in, after he got a job in Canada!
I also feel very uneasy when people are around mine - unless it's family or one of my 3 BFFs.
I think a lot of people feel the same. People who do feel like this get bashed to fuckery on here though by the people who invite the world and his husband around, and also tend to pop in uninvited to people homes whenever they like, and get sniffy when people don't welcome them with open arms.
Upshot is, invite them by all means, but don't be offended if they don't say yes. Some people simply don't like socialising with neighbours.
Moreover, virtually ALL neighbour disputes are between neighbours who were good friends before. It's rarely between neighbours who have had very little to do with one another. So I think this is the reason why many people don't like to socialise with neighbours...