Dealing with an obsession is like dealing with any ghost from the past: you either have to confront it or forget about it to make it disappear or to stop it from haunting you. You don't know her, so she's taken on a mysterious, ghost-like quality and you probably think she's far more beautiful and amazing than she really is. If you find yourself becoming obsessed with her, you need to sort yourself out before you can sort his obsession out. Don't avoid her: it'll do you good to see her so that you can tell yourself she's normal and not a 6-foot Scandinavian sex goddess. Stop trying to compare yourself to her or trying to be like her: he chose you for who you are and probably precisely because you are different to her. She's your past, but you're his future!
Never try and be too matey with the ex that won't go away - it'll be totally false. You shouldn't be that interested in his past and vice versa. If they're still friends then it's great there's no bitterness between them: very often if there's still anomisty between exes it means they still have strong feelings and/or unfinished business between them.
However, if they've only just split up and they're still seeing a lot of each other, it might be a good idea to suggest they stop seeing each other for a while - at least until you're settled in your new relationship. This will help everyone to clarify exactly where they're going and what they want. No-one wants to be the 'rebound' or the 'transition' between relationships, so you need to get things straight: if he's not over her, you're not going to play second best.