Hi, I too am in H4 and arrived VA 2 months back. I managed to take learners permit. In addition to my  passport i submitted appartment lease agreement in which my name was mentioned too... so i was easily permitted to sit for the exam, hope this will help you too.. coz you too are applying in the same state ie VA. And while applying for Learners permit  for your spouse they need your passport and original I-797 too. cheers and have a safe driving.