is he willing to take his meds for the bipolar? if they're not working, if has some prescribed, he should discuss this with his post doc.
the situation is beyond your control. if he is willing to get help things may change for the better. his infidelity has really clouded the situation, imho.
i'm sorry life is so tough for you right now. i agree, take a break if you can and distance yourself from his mental heath issues. if he doesn't get help and follow their suggestions, then you can make decisions re your marriage.
as for his lying about your status in the marriage re leaving-don't worry about what other ppl think. what is important is you know the truth. you've done nothing wrong.