Since your home has no equity, you could file for bankruptcy and eliminate your unsecured debt without losing your home, as long as you can make your mortgage payments.
If you believe that your property will someday have equity value again, then you would want to choose Chapter 13, because title to the property belongs to you after the discharge.
If you believe that your property will always remain underwater, then Chapter 7 is a better solution, because you don't have to make payments towards your unsecured debt. You are just discharged from all your debt immediately. However, the bankruptcy trustee can choose to retain your interest in the property, so that if it is ever sold, the trustee gets any profit.
Hope this helps.
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Nevada is a community property state. This means that if only one spouse files for bankruptcy, creditors can sue the other spouse to collect on the bankrupted debts, out of the spouses' community assets. So, while one of you can legally file bankruptcy separately, it won't really protect you unless you file jointly.
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