Both my husband and I have an iPhone 4. When my husband tries to use his ID on his phone mine will pop up and he can't change it. When he goes into his settings his ID is there. This only started when I plugged my phone into the PC.
Can 2 ID's be run from the same PC?
As the other posted have said, this is an incomplete question, but I infer that you have installed apps from each others' Apple IDs to the same phone. For example, if I am running iTunes as my own ID on my phone, but I try to update an app that was purchased by my wife with her ID, I will be prompted for her ID and password in order to do the update. To me, this sounds like what you're seeing on your phone which you are both sharing.
To answer your question, yes, 2 IDs can be run from the same PC, just as 2 IDs can run on the same phone... but NOT at the same time. That's the key. As the posted shows above, only one ID can be logged into the Store at one time though.