If I look at the Bios settings in the user manuals of different motherboards, almost all of them indeed have the "Virtualization Technology: Enable/Disable" option, but only a few also have the "VT-d: Enable/Disable" option. This makes me think that your statement that most motherboards support it only applies to general virtualization (VT-x), but not to I/O device virtualization (VT-d).
Meanwhile I have found 3 boards that do support VT-d and Dolby Home Theater: The GA-X79-UD series. Unfortunately these motherboards seem to have been shipped initially with a Bios (F7) that only supports 2 CPUs (i7-3930K and -3960X), which both happen to NOT support VT-d. If I look at product reviews on Amazon or Newegg, this has lead to many people not being able to use their board with a different CPU as you can't update the Bios if you don't have one of the two above mentioned CPUs. Since I don't feel like wasting money on buying two different CPUs, one of which will go right to storage after 2 mins of use, I'd rather avoid these boards.
If it wasn't for this problem, the GA-X79-UD5 would actually seem perfect for my needs, since it also has the PCI-e slot in the right position to fit the riser card in my Thermaltake Mozart Home-Theater case, but unfortunately it is the board with the worst reviews of the three.