Mąż - Husband.
Żona - Wife
Małżeństwo - Wedded couple, bit like 'husband and wife'. It allegedly comes from "Żenić się" (to take a wedding / to take a wife, depending on context and speaker) and old germanic "Mal" meaning "pact". So it's a one word that, if this etymology is correct, means "a pact of marriage" or "taking a pact with your wife"
But as far as calling each other, we do have possessives (Moja żona - my wife / Mój mąż - my husband. Note the different suffixes for genders, that's how we do it by the way) but it's incredibly formal and unusual. Just like in dating, you can say "jesteśmy razem" (we are together) or "jesteśmy małżeństwem" (we are a married couple). In formal situations it's perfectly correct to use "Moja żona" / "Mój mąż".
Also, almost all wedded couples here (even people not much older than I am) wear matching wedding rings, so that's a good way to spot married couples. As in regard to homosexual couples… I have no idea. I don't know enough and my country isn't as liberated. In part because of the previous reasons and in part because, despite stereotypes, most Poles are pragmatic enough to not look for problems in a language where almost everything depends on context, speaker's gender and object's gender. :P
EDIT: Sorry for belated corrections. I'm after my Swedish exam and language circuitry has not aligned yet. I've erased some incorrect or redundant bits and replaced repeated words with synonyms if anyone is interested. Either way… Jag klarade de provet med glans! :D