The IRS rule is:
Persons not eligible for the standard deduction. Your standard deduction is zero and you should itemize any deductions you have if:
• Your filing status is married filing separately, and your spouse itemizes deductions on their return
https://www.irs.gov/pub/irs-pdf/p17.pdf. page 93
The rule says nothing about how a person filing HOH must claim their deductions. You are allowed to file HOH and claim any deduction you want, itemized or standard. His choice has absolutely no effect on you, because you are not filing MFS. But your choice has an effect on him, because he is filing MFS and is subject to the rule above. (The application of the rule is different when both spouses file MFS.)
In short: If you itemize, he must itemize. If you claim the standard deduction, he can do whatever is best for him.
Secondly, the order of filing has nothing to do with how the rule is applied. The rule is what is written above. Order of filing might block someone from e-filing, if there is a conflict with a spouse who filed first. If that happens, and your return is correct, print and mail the return, and the IRS will straighten it out. But it doesn't apply in your case.
