To me each relationship is separate and should be treated as such. I strive to be as honest as possible with both of my partners, but if they were to tell me something in confidence, I would respect their privacy. Generally speaking, they've never asked me to keep something from the other, but we were all close friends before becoming more.
If sharing everything with your partner is important for you, than I'd suggest that you let any knew potential partners know this at the outset and let them decide if it is something they can live with. But I would not just assume that it is okay to tell another partner something my partner told me in confidence.