My oldest is just about 12 and has stayed home several times in the last couple of years by himself if needed. I don't, however, leave him and his brother alone.
I don't think I could ever leave any of my kids home alone "together" without another adult around. I wouldn't trust that.
My oldest is only alone at times when he is sick and I have to take the other two children to school or run a quick errand and he doesn't want to go for some reason. It's not often at all. My kids always like to go everywhere with me and never ask to stay home anyway.
Is there a reason your husband is so adamant about your daughter staying alone in order to become more confident? She is quite young and unless she is just asking to be left alone then why force her to do it? I guess I just don't understand that part. There are many, many ways to raise a confident child and still be there by their side the whole time.