I think both opposite-sex and same-sex couples should say "my husband," "my wife," "my boyfriend," "my girlfriend," etc. -- if they identify along traditional gender lines.

If nonbinary or agender folks prefer using "my partner" to describe their relationships, that's fine too.

When I'm married, I will be saying "my husband" to describe my man. I refuse to turn myself into a second-class citizen by saying "my partner" while married heterosexual couples simultaneously get to say "my husband" or "my wife."