If this sort of remark from your husband is something totally new, I think you should not say more about it right now.
Try to treat it as if he just was grumpy, or perhaps had misheard or misunderstood your conversation with the neighbour.
If he continues to make similar remarks when he chances to hear a conversation with another person, then I would start wondering how I should react if I were in your place.
Years ago, my husband heard, or rather misheard, part of a telephone conversation I was having with an acquaintance. When I explained what we actually been talking about, he realised it in no way had anything to do with his behaviour (which he had thought) and we never again had a similar discussion.
Your account made me wonder if your husband's hearing may be becoming less acute? Did he actually hear what you were saying, or did he assume he heard something you did not say?
It seems he overheard a completely innocous conversation and misunderstood the detalis of it. If this sort of thing continues, you may feel you have to consider whether his behaviour is changing in other ways too, and why, but honestly it does not sound so serious to me.
I understand why you feel you have been treated like an erring child, but you could turn it round and say your husband was eavesdropping on a conversation he had no right to be listening to!