Spouses can file individually or jointly. Whether you file individually or not, you need to report both of your incomes on the petition. That will probably not be a problem. With regard to the student loans, most are not dischargeable. Unfortunately, your wife will probably be stuck with them. If your wife used credit cards to finance school, those would be dischargeable. If you are behind on your mortage, you may need to file a chapter 13 through which you make regular payments toward your debt over a period of years. Practically speaking, most of the payments likely will be applied to your mortgage and other secured loans.
You need to see a bankruptcy lawyer for a free consultation. Most let you make payments and will file when you pay the full fee.