I refer to mine as Hubby. I never thought about why but it sounds better than "the husband". The Husband sounds like it should be the title for a movie.
Hubby never referred to me as "the wife". With him it's just "my wife" or "Livvie".
"The wife" kind of makes it sound like they're putting her in the same category as "the car" or "the boat".
I've heard examples such as: "How did you and the wife do on selling your vacation property?" Or "I let the wife know your party will be planned for this weekend. ~
I have heard that usage but never thought anything of it. Just as I have heard (not recently) "the parents".
I do think many of us tend to view a husband as an achievement - we don't get married every day - so is something we are proud of rather than just something that we can replace. I waited 53 years to have a husband. So we are more likely to say "my husband" or, with people who know him, mention him by name. I think that is more affectionate.
Might depend too on who is our audience. Talking to another man there might be a sense of oh yes that is what wives are like or what they do. Where when we talk among ourselves about our men we are more likely to mention certain behaviors and chuckle affectionately over them and that is one way we bond.