Is it normal for a husband to send a message to his girlfriend?

That depends on the circumstances under which your husband sends a message to your girlfriend. If something really happens or you send a message at your behest, I think it is normal. If he sends a message to your girlfriend behind your back, I think it's abnormal. It's possible, but it doesn't rule out that he may want to surprise you, send a message to your girlfriend just to know what you like, and so on. It's possible, but I think the high probability event should be that he has a different relationship with your girlfriend, and there are things he doesn't want you to know, and he doesn't want you to know. So if I were you, I might have a good talk with my best friend and see what they are like.