They are not supposed to do that. If you are married, you can only file either "married filing jointly" or "married filing separately." If either of you get audited, you can be hit with penalties and added taxes. Furthermore, because there are limitations on the deductions that you can take when you file married/separate, it is likely that a substantial deduction would be disallowed should you be audited. This would result in a potentially heft tax bill. Going forward you should file correctly and you may want to consider amending some of your past returns. Consult with a tax attorney who can best advise you on what to do about the old, incorrect returns.
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You should only filed "married filing jointly" or "married filing separately", and failure to do so could result in some fairly significant interest and penalties upon examination by the IRS. You should get with a qualified accountant immediately and have them calculate your exposure should you be audited, and after those calculations are complete, you should consider amending your prior returns.
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When you are married you have a year by year election to make to either file as married or married filing separately. Head of household is not an option.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.