If he is filing a married filing separately tax return, he needs your SSN in order to efile his return. If he doesn't enter it on his return, he can't efile it. He should not be filing a married filing jointly return since you are filing Head of Household.
The tax law says that he must enter the spouses SSN on a Married Separate return. The IRS can impose a penalty on you for failing to provide it.
If you don't file your return and pay your tax by the due date, you may have to pay a penalty. You may also have to pay a penalty if you substantially understate your tax, understate a reportable transaction, file an erroneous claim for refund or credit, file a frivolous tax submission, or fail to supply your SSN or ITIN. If you provide fraudulent information on your return, you may have to pay a civil fraud penalty.