A PCI bridge shouldn't even need a driver. They just work, like the ASM1083 did in previous kernels. But the chip is buggy, so you have to copy Windows's behaviour on PCI bridges to get it working, instead of just following the specs.
Nearly every chipset has a PCI bridge built-in. I know two exceptions:
Newer Intel chipsets lack PCI so they use a third-party chip.
SiS has an entirely different configuration on their chipsets. The OS talks directly to the PCI devices, through the northbridge, and doesn't know that the southbridge's PCI bridge is in-between. This works fine on Linux, including IRQs.
All those PCI bridges in chipsets just work. Intel, AMD, nVidia, all working fine.
I'm sorry. Most ITE devices on motherboards are Super I/O chips but they also appear to sell PCI bridges. I had never seen those chips before while ITE I/O chips are quite common, also on motherboards where the PCI is built-in into the chipset.
The chip is, however, not listed on ITE's webpage. I couldn't find any official documentation on it.
I've removed my previous post.