It depends on the situation, the people we are with, and the "comfort" level as to whether it is necessry to reveal such private information.
We live an outwardly straight life, nd have done so for more than 20 years. Only a small number of very select and trusted friends know our situation. so, you can say we are very deep in that well known closet. And, we (he more than I)are quite comfortable there.
If it is within a group of people with whom we "both" (and I stress "both")feel comfortable, and a qualification is indeed necessary, then I usually introduce him by his name and add, "my life partner." But, usually I just give his name with no further information provided.
In other situations, he is just introduced by his name.
"Husband" I dislike since it implies marriage and that I am the "wife" ( and v.v.), which I find extremely offensive.
"Spouse" also implies marriage.
"Boyfriend" I could have used when I was a pre-teen, but not now.
"Partner" could be taken as a business relationship.
"Lover" is too....well I just don't like it since we are so much more to each other than lovers!
"Sigificant other" and "Mate".... implies you couldn't think of anything else.
However, "Friend," and sometimes "Best Friend" (depending on the situation) are good catch-all terms and I use them a lot, because we indeed are Friends....and Best Friends.