Ancient Greeks certainly did get married and it was a fundamental part of their social structure, highly formalised and steeped in tradition and symbolism.
Homosexuality in ancient Greece was not quite the same as we would term such today either, the most common and the generally accepted form of homosexuality in Ancient Greece was in fact Pederasty, something which is illegal in most countries today. Adult homosexual relationships in Greece also had social stigma attached to them, particularly for the less dominant partner and always formed a Dominant-Passive relationship rather than one of equals, with the masculine partner being the dominant one and the feminine one having the social stigma attached to them. While the Pederastic relationships were formalised and could be considered a form of marriage, they were temporary, ending when the boy was 17. Adult homosexual relationships did not have the same formal standing as heterosexual ones.
However the Romans did perform same-sex marriage unions, however once again they did not have any formal legal status and were not considered the equal of heterosexual marriage. (it was considered on the same lines as a relationship with a slave, with one partner being the dominant one)
While homosexuality was considered in a far more liberal way, particularly amongst the higher social classes in Ancient Greece, it still was not as accepted and commonplace as some would like us to believe and is not really a comparison to what we are heading toward today, with equality under law.
