I had this exact setup about two years ago. I had DirecTV, then added FIOS internet. Verizon actually provided DirecTV as the TV service wherever FIOS TV had not been provided.
I had one bill, for internet and DirecTV. When the FIOS TV service became available, I made the change fast, but I don't think there would have been any trouble in keeping DirecTV.
Just an observation, but FIOS TV has been quite the improvement over DirecTV. Of course, I switched from SD on D* to HD on FIOS.