Same sex "marriage"

In today's Journal.ie there is a report of the the partner of the Guardian journalist who worked with Edward Snowden to expose US surveillance tactics being detained for almost nine hours under British anti-terror legislation. The report is headed "Husband of journalist who broke NSA leaks story held for nine hours in London". I did not know that these people were in a same sex marriage and had to read down a bit until I realised this. Is the term "husband" the correct one to use in this case? The husband referred to is David Miranda. Is his partner Glenn Greenwald, his wife?
I support equal rights for same sex "unions" but we have to get our terminology right when referring to the participants therein. I have doubts about even calling the the relationship marriage. I am open to persuasion in this matter.