A roving eye I haven't heard of, but I have heard of a roaming eye. That is when (usually a man) person will watch other people of an opposite sex (usually a woman) and follow them with their eyes even though they are in a serious relationship (including marriage).
Example: A married couple eating dinner at a nice place, and a good looking younger (usually) woman walks by. The husband will follow the woman with his eyes, ignoring his wife....and pissing her off. Anytime they are talking and a woman walks by he will seem to do this. That is a roaming eye.