This is a good question. There are a few points that will help in answer this question.
First, one of the things that is common among the gods in Greek mythology is that they seems to always sleep around with each other. So, this episode with Poseidon should not surprise us. Athena is particularly ticked off however, because Poseidon was with his girlfriend in Athena's temple. Athena takes offense at this, because Poseidon did not respect the sanctity of her temple.
The girlfriend that is in view was Medusa. As a punishment Athena turned her and her two sister (who helped her) into gorgons. Anyone who looked at her would turn to stone.
Second, it is also helpful to keep in mind that Athena and Poseidon did not like each other, because both wanted to be the patron/patroness of Athens. As you can tell, Athena won out.
Also, in the film, Medusa smells Percy and puts an emphasis that he is the son of "Poseidon". Potentially this could help in infering that Medusa dated Poseidon.
It was a date between Medusa and Poseidon.
In the book and film it shows that Medusa wants to take her anger out on Annabeth because she is a daughter of athena and athena is the one who turned her and the other gorgons ugly. Also it tells how medusa doesn't want to tear Percy's face apart because he reminds her of his father, Poseidon. Therefore by deduction and the fact that Poseidon and Medusa did date, they had Pegasus and Chrysaor, they were also caught in athena's temple, probably because athena became the patron of athens instead of poseidon.
the girlfreind is medusa