No.
If you file as Married Filing Jointly (MFJ), she will effectively have half the income (but not actually, it's still entered as your income). Using any other filing status (HOH or MFS), you must report your income and she must report hers. There is an exception for community property states, but then she would report only have your income.
What makes you think either of you, or both, can file as Head of Household (HOH)? It's rare for one married person to qualify as HOH, and incredibly rare for both spouses to qualify.
