Thor,
I do get some DD5.1 broadcasts on the premium channels (HBO). I have Charter Communications, and a Scientific Atlanta Dig. Cable Box. It has both analog (rca) left/right, and digital coax out. Both must be hooked up on mine. If I only hook up the dig. coax, I get no sound on analog broadcasts. I have both hooked up to my AVR, and set the TV input on the AVR to auto-detect a digital signal.
I'll occasionally find Dolby Digital 2.0 broadcasts on some channels as well.
But it sounds like your cable box doesn't have a digital connection. You'd need a dig. coax or fiber optic (toslink) connection for digital broadcasts.
If you are paying for digital cable, then demand a box that has digital outputs. After all, you are the customer.
JD