I think I've just had this question answered by iDine.

I belonged to Transmedia and also had my credit cards registered with United's dining program. When I used my Transmedia-registered credit card recently, I found I did NOT receive any cash credit towards the bill on my online credit card statement.

After sending an email to iDine to ask about the credit, I received the following reply (exact quote):

"When Transmedia and Dining a la Card merged, your existing accounts were merged together. You have a Frequent flyer account with Dining a la Card. Now that the 2 programs have merged, you will receive 10 frequent flyer miles on the first visit to a participating restaurant. Then on your second visit, you will receive your monetary savings."

I'm not sure I like their solution, since I'll never be able to keep track of whether I'm getting miles or cash, so I think I'm going to cancel one of the two methods -- I just haven't decided yet which one. I love the miles, but the immediate cash discount is hard to pass up.