Only time I used my personal card by default was when I worked at a startup. Generally company policy when they issue a card is that You Will Use The Card We Give You, And That's Final.

I wouldn't bother trying to use your own card. There's a reason they give you the company card in the first place. Besides, if their reimbursements run a little late you might be stuck floating the firm with the cash for a hefty bill.

Still, if it's that important you could have your wife check the employee handbook. The expenses section will probably mention using company vs individual cards if that's an option. If not, see if you can at least sign up for the company card's rewards program. Most places I've worked that issued cards let you sign up for the Amex Membership Rewards on the card - some firms even paid the membership fee for you.