OP, my hubby & I were in this situation not long before we got married. My friend who I'd known for years had been with my DH's friend (who DH had been besties with for quite a few years) - in fact they were engaged for 9/10 years and introduced me & my DH.
DH & I met, got engaged and then married in a very short time - just over a year - when its the right one its the right one. Anyway shortly after we got engaged my friend and her OP (my DH's friend) split. It wasn't that nice. I think it had been a long time coming as they seemed to be very different and not have alot in common - but either way that's not really my business. But the split was painful for my friend - she was the one betrayed.
DH and I cared about both of them and we did say at the time to both, that we wanted to remain friends with each of them, that what was said by one would stay confidential and we would support both. We really meant that.
I don't feel that anyone should stay in a relationship or marriage that isn't working. Each person deserves to be happy and to be with someone special. Although I agree with another PP that if you aren't happy, have tried to mend things and it doesn't work, then you should leave the relationship before you start looking or going with anyone else. That is behaving with dignity and honour and treating the other person you don't love anymore with respect.
Anyway, in this particular case it wasn't pleasant, but despite staying neutral and supportive, my DH's friend was the one who basically dropped us. Perhaps it was guilt and shame over his bad behaviour - he was horrid to her financially and with cheating, and perhaps he couldn't believe we weren't judging him - he wouldn't even come to our wedding because my friend was coming. But 20 years on, we have lost touch with him, and we are both still friends with my friend. Trying to stay neutral and support both didn't work.
Other times when friends have split from husbands, I've not tried to be so liberal. Sometimes, the person who is hurt, dumped and made to feel worthless by being rejected just needs to know that her friend has her back. They need to hear the words that the other person is a complete sh#t, and isn't worth the tears. They need the coffee, cake, bottle of wine and girly sessions and to be told they are going to get past this and meet someone who is worth being with. And I don't think there's anything wrong with that. I'm just helping a friend through a terrible trauma.
OP, I don't know if you became friends with this lady because she was married to your DH's BF, or if you were friends with her anyway. But either way, she has obviously been your friend for a long time, and her soon to be Ex has been your DH's friend for a long time.
None of us here know the situation with the new GF who met who, when, during etc. No-one knows if this man met the GF before or after the split, or whether she knew or not. That isn't for us to know. I guess if it was me any 'judging' on my part re GF would be whether she knew he was married but got together with him before he left his wife. That would mean a complete no no to any meeting up in the future as far as I'm concerned.
But in the current situation, I think you need to sit down with your DH and explain that you aren't asking him to stop being friends with his BF but that you are staying friends with his soon to be ex wife and intend to support her through what is a terrible traumatic time. If he would like to support his BF's Ex and be non partisan and hear her side of it and how his friend's actions have affected and devastated her, then he's welcome to do so, - try the 'we will support both', but if he understandably doesn't want to do that, then both of you need to each agree to support the friend you have chosen. And that unless he wants their breakup to start affecting your relationship he needs to respect boundaries. i.e. DH doesn't discuss with you about his BF or the OW, and you won't pass on confidential information about your friend. I think I would be inclined to say that you can't imagine at the moment when you would want to know or have anything to do with his BF and OW, but that may change over time and as your friend gets over what he has done. But, I would stress, that you will be the one to let your DH when that time has come for you, if it ever does. In the meantime you would appreciate it if he sticks to the agreement and keeps his relationship with his BF and the OW separate from you.
I hope that both your friend and your DH's friend get to move on, and meet someone who is really special and who treats them with all the love and care they deserve.