Perhaps the biggest misconception regarding filing bankruptcy is the notion that upon filing, you will lose all of your property. This couldn't be further from the truth, as in most Chapter 7 bankruptcies you will get to keep all of your property.
When you file a bankruptcy, a bankruptcy estate is created. All of your property is technically included in this estate. In a Chapter 7 bankruptcy, it is the bankruptcy trustee's responsibility to analyze this estate to see if any of the property can be liquidated. However, there are state and federal exemption laws that allow those who file bankruptcy to protect the value in their property ahead of time. These laws cover value in property that otherwise might be unprotected.
As a result, then, filing a Chapter 7 bankruptcy does not automatically result in the loss of all of your property. As long as you continue to make timely payments on both your house and car, you won't lose that property either. Prior to the filing of the case, most of the property is protected from either state exemptions, federal exemptions, or both, depending on the state. Most of the time, then, you will not lose any property whatsoever on your path to a discharge of your unsecured debt.