My husband is at work but I’ll check later to confirm this:
My husband has dual citizenship, US and ROC. He’s on the household registration (I’m a foreign spouse, and the kids and I are now on there too).
When we first got here just about 3 years ago, we all entered on US passports. Then after getting a job, he exited with our son and they both re-entered… I think the little one entered with ROC passport, and dh entered with US passport.
Now our son can live here, but dh has to exit and re-enter the country every 4 months. For work, he uses his Taiwan ID and pays ROC taxes.
I could be wrong about the passport he enters the country with, but I’ll check to make sure. If you’re American, have you checked the AIT website? I’m pretty sure I saw something there about dual-citizens and those avoiding the military service.