[quote Dinoasaurme]@Straightupp gosh that sounds really hard for you. I'm really sorry you're dealing with this. But in my humble opinion I really do think it's not on and as PP's have said, it is abuse.
Like the pp up above @TheGrinchsDog I have experienced a lifetime of unhealthy and abusive or coercive relationships as a direct result of this style of "parenting".
Your husband is cultivating an embedded deep sense of shame within your child- shame that they are fundamentally wrong or faulty, that there is something wrong with them. This won't even be a conscious thought, just a deeply held belief which, if he is left to carry on raising your child this way, will be with her for the rest of her life (only unravelled through years of therapy in my case and still requiring daily work).
His criticisms of her and his shaming of her with the shouting or punishments will be being internalised by her. Adult children of emotionally neglectful or abusive parents carry round with them an inner critic, (their parent's voice) which chips away all day everyday about every micro decision they make, essentially saying "you're not good enough / you should be ashamed / you don't deserve X / you are not worthy" etc etc.
Also, the lack of self worth and feeling of shame will result in the adult child gravitating towards other abusive men, friends who take advantage, and even bullies in the workplace. The "blueprint" for what love and care should look like has been modelled by the parent who was abusive. Therefore the adult child simply replicates that blueprint throughout their adult life, until it destroys their life or until they hit rock bottom and there is an intervention.
Also, whilst you may feel better able to protect her if you stay with him, what that actually does is teaches her the lesson that he is ultimately right. Because whilst you may be the kind parent, you are still honouring this man by having him as your life partner and in your family home set up, and that's telling her that ultimately you condone his words and behaviours, reinforcing his bullying just by you sticking with him, even though you don't parent that way, if you see what I mean.
If he left the marriage and the family home you would look after her. He may not be allowed to look after her by himself. Even if he did, you would be the main parent and as she grew up it would be your influence and your voice she would be shaped by.
Please think about it. Sending you hugs 
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All of this ^ Twice if necessary. Dino has articulated a lot of what I wanted to say and couldn't.
@RachelGreeneGreep Thank you, that's very sweet. I'll be alright.
I so wish other children didn't have to go through similar but so many do. It is life altering damage, these parents should be kept as far away from their children as possible IMO.