Generally, you must file as married (filing jointly or filing separately). HOH is certainly not designed for your situation, and you would have to push the definition of "considered unmarried" up to or past the breaking point.
In the past, some taxpayers posting to this forum have attempted to play word games with #3 in the last section, "Your spouse didn't live in your home during the last 6 months of the tax year." A simple reading of this would suggest that as long as you don't spend even one night in the other spouse's home between July 1 and December 31 (your intimate moments would have to be arranged for a third "neutral" location) you could qualify. But I think that an auditor would look at your overall situation to determine if you could be considered unmarried under the laws of your state, and if you are legally married and act in public as if you are married and you hold yourself out to other people in society as being married, then the IRS would consider you married.
From IRS publication 501:
Considered married.
You are considered married for the whole year if, on the last day of your tax year, you and your spouse meet any one of the following tests.
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You are married and living together.
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You are living together in a common law marriage recognized in the state where you now live or in the state where the common law marriage began.
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You are married and living apart but not legally separated under a decree of divorce or separate maintenance.
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You are separated under an interlocutory (not final) decree of divorce.
Later in the same publication, regarding head of household, it says,
Unmarried persons.
You are considered unmarried for the whole year if, on the last day of your tax year, you are either:
State law governs whether you are married or legally separated under a divorce or separate maintenance decree.
And lastly, publication 501 says,
To qualify for head of household status, you must be either unmarried or considered unmarried on the last day of the year. You are considered unmarried on the last day of the tax year if you meet all the following tests.
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You file a separate return. A separate return includes a return claiming married filing separately, single, or head of household filing status.
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You paid more than half the cost of keeping up your home for the tax year.
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Your spouse didn't live in your home during the last 6 months of the tax year. Your spouse is considered to live in your home even if your spouse is temporarily absent due to special circumstances. See Temporary absences, later.
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Your home was the main home of your child, stepchild, or foster child for more than half the year. (See Home of qualifying person, later, for rules applying to a child's birth, death, or temporary absence during the year.)
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You must be able to claim the child as a dependent. However, you meet this test if you can't claim the child as a dependent only because the noncustodial parent can claim the child using the rules described later in Children of divorced or separated parents (or parents who live apart) under Qualifying Child or in Support Test for Children of Divorced or Separated Parents (or Parents Who Live Apart) under Qualifying Relative. The general rules for claiming a child as a dependent are explained later under Dependents.
