Excellent Question! I'm going through that decision process right now. I'm at a point where, I have to decide whether I can live with something that isn't likely to change. Is it something I can accept or is it a deal breaker? I really haven't decided yet. I know it will always be a problem and I will always push back on it. And, I know he will never change the offensive behavior. Part of that decison is - am I better off with or without him and are the kids better off with or without him? I haven't really decided that either. My life is so hectic, I rarely get quiet time to reflect. But, I weigh pros and cons almost daily.
To answer your direct dilemma, My husband is much more strict than I am. I frequently think he goes a bit too far. He always thinks I am too soft. Well, the proof is in the pudding. My kids love and respect thier daddy deeply. They love me, but they run over me. I can't handle them in public by myself. They frustrate me to no end, because they do stuff they never do when dad is around. All the time outs, consequences, stern looks, stern but compassionate talks in the world don't make a dent. Dad pops thier butt, whereas mom talks till shes blue in the face. The pop is much more effective. He, like your husband, also thinks kids need to fear the consequences. It sounds bad when you say they need to fear him. It's the consequences that they fear.
I think, it is time that maybe you think about signing both of you up for a parenting class. Not because you need a class in how to parent! But, so that you can have an impartial 3rd party expert say things. Your husband will put more weight behind it and act as though it's the 1st time he's heard things that you say to him daily! FUnny how that works. It may also suprise you to hear that your husband may be more right than he is wrong.