I understand the hesitation to file for separation. You can wait to do that if you are certain that he isn't filtering money out. I had a doozy of an ex and he ended up leaving me months behind in bills etc.
When I filed for D from LSS I found out that he had changed all the bills from both of our names into just my name (using the "or" thing talked about above) that way he could say that he left on such and such a date which left me responsible. He also did it for credit cards he opened in both of our names which I never saw. In my D papers, I named him responsible for all debt and then the courts told me that I could have had my name removed from any joint account if I had his social security number. I don;t know if there is any truth to that but it would have saved me about $3000 in debt had I known.
I woul ddef. open my own checking and savings account though.