Should each of us have our own savings or checking account?

My fiance and I live together. I think we should have a joint checking account for bills to include anything that has to do with household expenses, including car payments, clothes, medical bills, etc.
I also think we should each have our own checking/savings account for things each of us may want to save for....
Since I make about twice what she makes I think the bills should be split in some way like 70/30 or something along those lines. How does everyone handle their expenses?