Why do my pictures show up on my husbands phone?

You might have iCloud enabled for your pictures. You can leave it like that or disable it in settings if you want.

Most likely because you and your husband share the same Apple ID. You should each have your own unique Apple ID.

candy2812 wrote:

You might have iCloud enabled for your pictures. You can leave it like that or disable it in settings if you want.

Nah. They're sharing the same Apple ID.