People tend to base their parenting styles on the patterns their parents established with them when they were small and dependent, figuring they turned out okay. Or they'll sometimes adopt an opposite style, if they were extremely unhappy with the parenting they received. Either way, this is so deeply ingrained that we seldom find cause to question it.
But it's also true that men often like their choices to be based on facts, so why not get a good book on Emotion Coaching and read it for yourself (an excellent one is Raising an Emotionally Intelligent Child by John Gottman). In conversations with your husband, casually mention information about the studies showing that kids who are raised empathetically are more physically healthy and emotionally resilient, less affected by stress, perform better academically, have better relationships, and are less likely to develop behavior problems. If you're not challenging him directly, your husband may be able to take in and process that information, allowing him the chance to try something new when nobody's watching.
Another way to approach the problem is to establish a relationship with your daughter that is clearly authoritative, yet still kind. This would gradually show your husband that empathetic parenting gets good results, and if you are incorporating empathy, your daughter will handle her dad's harshness better – AND probably make it less "necessary" (from his point of view) for him to come down hard on her.
A fabulous resource for authoritative parenting (as opposed to authoritarian) is another extremely practical and easy-to-implement book called How to Talk So Kids Will Listen, and Listen So Kids Will Talk. I use these gentle techniques with my grandson, now 4.5 years old, and he seldom finds cause to resist my authority – or do anything but cheerfully cooperate. The trick is learning how to appeal to a child's need for some control and respect – and this book teaches you exactly how to accomplish that magic.