There are different answers for this depending on where in the story we are. At first they probably thought Julia was interviewing Barnabas about the family history since he had so much knowledge concerning this. This was during the time when [spoiler]they didn't yet know she was a doctor and while she was giving him injections and he was threatening her life every five seconds[/spoiler]
Then after they learned she was a doctor, there would be a difference in their perception of what they were doing with the time they were together at the Old House. Julia was often spending the night, or since no one ever sleeps at night on this show, they were busy dealing with whatever the present danger was. They realized Barnabas and Julia were working together on something, and based on what each character knew about the present danger, they'd either think they're working together to find answers or they were just spending time together as friends. If they thought there was a romance going on, they'd start to watch them while they were together. Since there were no looks of love or romance (at least on Barn's part) maybe if they were astute, they'd realize that Julia loved Barnabas but he did not return her affection. It seems that no one decided to step in and help matters along though, like maybe suggesting that Barnabas take Julia out to dinner or even plotting such a thing themselves. They were always too busy with the present danger to think of such things as this.
Alondra