Employment Based Immigrant
A copy of an USCIS I-94 card or un-expired foreign passport with one of the following visa classifications:
H-1B, H-1C, E-1, E-2, E-3, L-1A, L-1B, P-1, R-1, TN, G-1 thru G-4, or
A copy of the front and back of an Employment Authorization Card as evidenced by an I-766, I-688A or I-
688B card containing the applicant’s photograph. Sometimes the numbers are on the border of the card,
so the copies must be clear.
Family Sponsored Immigrant and Visa Lottery Winner
A copy of an USCIS I-94 card with one of the following visa classifications: H-1B, H-1C, H-4, E-1, E-2, E-3,
L-1A, L-1B, L-2, P-1, R-1, TN, V-1, V-2, V-3 or
A copy of an Employment Authorization Document (EAD).
The above excerpt is from a FHA underwriting manual. I have closed many FHA loans with Visa's. They are actually easier than conventional. You must have a valid social security # and have a 2 year work history documented. The work history does not have to be in the United States.
You should have an EAC that was issued along with your visa. EAD's are much less common.
Hope this helps!