If you guys are looking for "the" right answer on this that's applicable to everyone, I'd say it doesn't exist.
I imagine a lot of you are religious so you have that standard you have to live by. "Integrity" is going to rank pretty high in importance for a christain or other people of faith. For everyone else, its only importance is how it affects your reputation.
I think, unfortunately, "integrity" is overgeneralized too much meaning a lot of people think you simply have it or you don't with no in-between. I personally tend to be more specific with the idea though. For instance, lacking integrity in your personal life doesn't necessarily mean you'll lack it in a professional setting. Sometimes there's a reasonable basis for being dishonest (aka lacking integrity) in a personal relationship that doesnt necessarily warrant one being branded as simply a person that "lacks integrity". Though i'm agnostic, i'm reminded of Jesus' words "He who is without sin (has no sin), cast the first stone". Thus, no one can claim perfect integrity anyway, thus its only a matter of degrees in which one lacks integrity.
I think it has a lot to do with personality too. Some people compartmentalize very well and others dont. If you're not able to compartmentalize, then your dual-life feelings and ideas are just going to spill over the mental boarders and just cause more mental havoc than enhanced life.
So, weight your faith, personal values, importance of integrity to you, ability/desire to compartmentalize, and ability to not get caught and make an informed decision. Sometimes that other person just isnt worth the risk anyway.