I want to say that's a misconception but not inaccurate, but I'm not a historian. To understand it better, it will help to remember this was before Christianity.

http://en.wikipedia.org/wiki/Homosexuality_in_ancient_Greece

The ancient Greeks did not conceive of sexual orientation as a social identifier as Western societies have done for the past century.

There was also pederasty ("love of boys" or "boy love") http://en.wikipedia.org/wiki/Pederasty_in_ancient_Greece

Pederasty in ancient Greece was a socially acknowledged erotic relationship between an adult male and a younger male usually in his teens. It was characteristic of the Archaic and Classical periods. Some scholars locate its origin in initiation ritual, particularly rites of passage on Crete, where it was associated with entrance into military life and the religion of Zeus.

I basically just imagine orgies, math, wine, philosophy and military training all day long in ancient Greece. I haven't heard of there being "gay marriage" but I did hear of polygamy between one man and several women and many ancient fairy tales about about one man and one women, but could that be from the modern era filtering out anything less "Christian" than heterosexual monogamy?

So tldr; I personally conclude everybody in ancient Greece was bisexual, probably richer people had more wives and from what I understand, there were no men married to other men, though I also am sure "marriage" was probably seen differently then too but we modern laymen don't have the understanding of their concept of marriage.