First, I'll get the obligatory caveat out of the way: "homosexual" is a modern designation and doesn't reflect the way ancient peoples thought about sex.

You are probably thinking of the Athenian practice of pederasty. I don't actually know how common this was in other Greek states, but in Athens it was fairly mainstream. Pederasty (what we would call pedophilia) was largely associated with education. Since there was no public school system, a young boy of the elite class, when he reached schooling age, would find a tutor. They would generally develop a sexual relationship with their teacher--the young boy was called the eromenos and the adult the erastes. When the boy grew up the relationship would end, and he would go on to marry a woman and become a politician or a general or what have you. Often they would eventually become erastes to another young boy and repeat the cycle. It was not totally uncommon for these relationships to last longer than normal, and some men were known to maintain the relationship for their entire lives.

An interesting example is in Plato's Symposium, a dialog on love that takes place at a party. Near the end, Alcibiades, a former student of Socrates, bursts in and starts getting jealous that Socrates now has a new boy. Two of the other characters are also described as committed lovers, one being the former student of the other.