Married filing Jointly (MFJ), even if one spouse has no income, is better than filing as Head of Household (HoH) or Married filing separately (MFS).
"Does he have to file, even if he has no income?" Technically, no (unless you live in a community property state). But in order to allow you (the spouse with the income) to use the best filing status (MFJ), he has to file with you. A spouse cannot be claimed as a dependent; he can only be claimed as a co-filing spouse.
As others have said. you are not allowed to use Head of Household filing status, in your situation.
In addition to all the other already stated reasons that you should file MFJ, you will pay less tax on your income. For example, the tax on $50,000 of taxable income* (from the IRS 2015 tax tables) is:
Single: $8300
HoH: $6846
MFS: $8300
MFJ: $6581
*"Taxable income" is the amount you pay income tax on after all deductions, exemption, adjustments and tax credits.