Is it really cheating?

My wife, unfortunately, is not much of a ual partner..she is a great mother, partner, companion whatever but in bed, she is there only to do what a wife does for her husband. I find that to be more of a turn-off than anything. I have even told her that she could go and have an affair! Maybe that would turn on her ual side if I am not doing something she needs...But, she says she is okay with the way she is. My problem is that i have told her that "the way she is" is a ual turn-off. When we do have relations it feels just like being served food or having my laundry done. She is doing it because that is her role.It sucks. And the problem gets worse. I work with a very attractive and y woman who has let me know we could get together discreetly since she is married. So..if i cannot get it at home...and it is a big part of any being...am i allowed these encounters if they are something I need that my wife cannot provide?