Maggie, I'd call it a big red flag for you to want to start any kind of a real relationship when you can't deal with the one you're in. I'm not being judgemental of your actions, or condeming them, just laying out the facts as you have presented them.
You are in a failed marriage. You are sleeping with someone else that made it clear this was purely sexual. You are still in this failed marriage and give no indication that you plan on doing anything to fix it or end the marriage, but you want to start up a relationship with someone else before you have finished your current one and processed what happened with it.
Scenario 1: Your FWB does want something more. You stay married and the stress of leading a double life eats away at you. If you have kids then they already know something isn't right and it will only get harder for them as you become more detached from your husband. Meanwhile, the guy you are with will eventually get frustrated being second on your schedule and having to wait for when you have free time so he does one of two things - Either he starts demanding you leave your husband or he states that if you don't decide between him or your husband soon he is gone. If he is a real jerk then he may even threaten to tell your husband about it. Either way, all things end in disaster.
Scenario 2: Your FWB likes things just as they are. You go along with the pretense that at least you're getting something with him that you aren't getting from your husband. The kids are still getting screwed up by this because all they know is you are drifting away somehow but don't know why and possibly start thinking its their fault. You still aren't getting the completely fulfilling relationship you want because eventually sex without real love or intimacy becomes pointless, petty, and some cruel means of getting back at your husband for whatever his deficiencies are. Eventually someone finds out something and everything blows up in your face, leaving you alone.
Best advice...stop the FWB all together. Either fix your marriage or get out of it. Spend some time alone figuring out what went wrong with the marriage, what you can do about yourself to see that it never goes like that again if you ever decide to marry again. But no FWB or dating or anything for awhile.
Maybe you have tried to fix the marriage but your husband is unwilling. Why deny yourself the freedom and right to go find someone that does completely satisfy you emotionally and physically, without having to hide it from the world?
Its your life. You decide how to live it. You control how happy you are, or can be. I know the choices aren't easy ones to make, but you alone have the power to make those choices. No one else can live your life for you. No one else is responsible for your happiness. That is all up to you.
Best of luck to you.
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It is possible, but in this situation someone would end up cheating on the other, mostly because God will not bless antoher union if you're cheating in one union, unless your husband and you are seperated and he knows that you're dating. Otherwise karma is gonna creep in at some point.
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