I found an article by Valerie Connelly confirming most of my advice in my previous post, but she as a radio talk show host goes a bit further.
I had not considered that someone might feel so comfortable in being interviewed by phone that they would multi-task by either working on their computer or washing dishes.
Ohhhhh, I have to agree that unless you want to appear unprofessional you should not have anything in the background going on. Your interview should be your sole focus for that period of time as well as making yourself and your host look good.
Her article was also cross posted on Ezine articles.