Yes, the two worlds can. It is possible. But note I say "possible," not "likely." It's awfully bold and reckless to assume that a spouse is not going to find out about something like an online relationship or real life affair.
"Unfaithful," as I think many of the above posts have pointed out, is a matter of opinion.
All that being said, in actual application the technicalities, definitions, and semantics are of little consequence. There have been plenty of times in my life life that I have been utterly impeccable in my actions according to the letter of the law, but I have blown the spirit of it straight to Hell and people I care about have been injured. Sure, I could argue out the rationale of my actions, but at the end of the day all I had was textbook defined self-righteousness and a lover with a broken heart.
The point is simply: assume that he will find out and go forward with that likelihood in the forefront of your thinking. Maybe not tomorrow, but eventually he'll figure it out. To move forward basing your decisions on hoping that he won't is reckless, especially considering the gravity of the situation (i.e. kids and a marriage to consider). When he does find out, your definition of cheating won't make any difference at all to how he feels. If he feels violated and wronged, the fact that you operated within the technicalities of your definitions aren't going to make him feel any better - are you going to be prepared to deal with that?
You know this man better than any of us do, and if you think that he would be understanding then maybe this is worth the risk. If you suppose this is a deal breaker for him but your need for this is more important than the relationship, again, maybe it's worth the risk. You're going to have to sit down and weigh out the importance of each part of your life.
Good luck, my hope for you is that this is something that can be negotiated with your husband. A pipe dream in some cases, I know, but sometimes letting your significant other in on the fact that you want to be with them but need other things is enough to encourage them to be brave enough to support (or at least condone) your journey.Again, good luck.