Julia was researching Barn's curse, attempting to formulate a cure. Remember when she told him how his curse fascinated her? She is a scientist, a researcher.
Barnabas on the other hand uses and abuses her.
Throughout the series, they went through quite a rollercoaster ride. We all know how Julia felt about Barnabas and that he didn't return her affection. My personal opinion is that "nothing" happend by way of romantic interludes. I think towards the end of the series, Barnabas found that he had indeed romantic feelings, but was hesitant for one reason or another to act upon them. His only love as far as he is concerned is Josette and Julia didn't fit the bill. She is simply too much a "today's woman".