I don't think there actually is a "married" relationship option. They're talking about the "Lovers" one. There's 3 different relationships from what I've read Friends, Teacher/Student, and Lovers.
They all give various attacks and/or buffs, spells, whatever. I don't think that you can actually use them at will though. Rather they're triggered in certain situations, like for instance, you gain an attack buff if you Friend's HP drops below a certain amount, the "Helping Hand" buff.
It's really a pretty cool system that adds something new the mix. I like the idea, but in all fairness they should allow for same sex lovers, but there's not much to be done about it. Maybe write a letter to the NA publisher asking for it to be implemented. I reckon if they got enough they might take the hint.
Here's the DomoWiki page on Relationships:
http://www.domocamp.com/wiki/index.php/Relationships
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