Married couples have various ways of organizing their finances. Some use a pooled joint account for all their income and expenses, others keep totally separate accounts, and still others use combination of those options. Whichever method is used, it is important for the couple to discuss budgeting, preferably before they get married or live together.
Keep in mind that in divorce, the separate bank accounts may still be considered marital property, depending on the source of the funds. If you really want to keep your accounts totally separate, the best course is to enter into a postnuptial agreement. Postnuptial agreements need to be carefully drafted to be enforceable, so you will want to consult with an experienced attorney.