Percy, aka the epic hero, is a "demigod," meaning one of his parents is a god/goddess. Just like Aeneas mother is Venus. In Percy's case, his father is Poseidon. More than a few times Poseidon comes to Percy's rescue to help him fulfill his prophecy, just as Venus does for Aeneas.
Some might say that that Richard Riordan, the author of the series, does a disservice to the mythology he incorporated and modernized his novels. However, I would have to disagree. Let's face it, I don't know all that many people, besides various teachers and Joey, who are completely familiar with Greek/Roman mythology. By taking mythology and creating it into something that interests kids of the 21st century- Riordan, J.K. Rowling, and other authors are preserving these epic tales in the most creative of ways. Miranda and I read this series and had no idea until recently just how much knowledge we actually had on Greek and Roman mythology.