Yes, you may be allowed by the officer at the point-of-entry to enter on the approved H-2 visa even though you currently have a multiple entry B-1 visa stamp in your passport. However, the CBP officer, upon issuing you an H-4 I-94 entry document, will, in all probability, cancel your B-1 visa stamp "without prejudice" upon entry in your H-4 classification. You may be approved for more than one non-immigrant visa classification, but you are authorized to use only one visa classification at any given point in time.
Answered on May 04th, 2012 at 4:46 PM