You can't both claim the same mileage. I suggest that one of you claim the mileage and the other not claim any car expense for that day. Do you each have a car that you use for your respective businesses? If so, claim the mileage under the business that has other mileage for whichever car you use for the joint trip. Another option would be to each claim half of the actual mileage, or split it in any way that seems reasonable to you, as long as the mileage that each of you claims adds up to the total.
