For a married couple filing MFS is almost always the worst, most expensive way to file. With separate returns you do not qualify for many of the credits you might otherwise get if you filed a joint return.
When filing separate, if one of you itemizes deductions, then the other must do the same - even if those itemized deductions are ZERO. Likewise, if one takes the standard deduction, the other must follow suit.
The IRS needs your spouse's SSN so they can cross reference the tax returns to confirm you are both doing the same. I highly suggest you file a joint return. Based on the information provided thus far, filing separate will cost you more in tax liability.
As for what one of you may owe to the government, what is the debt for? Back taxes? Child Support? This is no reason to not file joint. The spouse who is not liable for the debt can file an injured/innocent spouse form with the joint tax return, and that will exempt the tax on that spouse's earnings from being taken for the liability of the other spouse.
The injured/innocent spouse form is included in the TurboTax program. To get to it, select the "Other Tax Situation" tab, then scholl down to Misc Tax Forms, click it, and you'll find Injured/Innocent Spouse there.
