Thanks @Adam RS!
He was exempted and had the card (+ official translations).
As for documents, just the ones listed really: Birth Certificates, Passports, Police Certificate, Marriage Certificate and the exemption card. He did Ask if I have a job offer as I mentioned, but was OK with me not having one. My lawyer had given me a memo in case I am asked for job offer to show that my category is NIW but I didn’t give it because both officers knew and I think even mentioned my category.
The second officer asked about Iranian experiences, the current company, the reason for his exemption, if we have entered US other than that on student Visa, if we have overstayed, where we want to live. I think that was it really.