HI

Two months back I went to the SSN office to apply for my wife SSN under H4 and they clearly said H4 depedent can not apply for SSN. So all you can do is do to nearest SSN office and ask the officer a letter or proof why SSN is not given to H4 dependent and show that letter to concerned authority. Then in that case, ITIN might work.

Good Luck..Amen