You can submit an online extension and just leave your spouse's name off the form. Nobody has to sign or report their filing status on an application for extension.
If you prefer, you can include your spouse's name on a paper extension, and list his SSN/ITIN as "Applied For". Refer to IRS Form 4868: Application for Automatic Extension of Time to File U.S. Individual Income Tax Return, complete and print the form, and send it to the IRS address for your state.
