I understand you. I had the same feeling. I wanted to know more about my T's life. Then I googled her on facebook and found his boyfriend too. I wanted to see photos of him...His page was private, there were some past photos. There was a photo of him and her kissing (it's his profile pic so I could see it). It wasnt a good thing for me to see that...I wanted to know more about my T, wanted to see how her life was, but at the same time I felt jealous (when I saw the kissing photo for example). I don't know if I'm jealous of her boyfriend, or about her life in general that seems perfect, beautiful and stable from the photos.
But I don't think that seeing her boyfriend was helpful to me. Yes, now I know what he's like...but it gave nothing to me. I don't know his personality. I'm more obsessed now after seeing that photo, I still have the habit to check her and his facebook page...it's not helpful.