Can photos taken with my iPhone (and Apple ID) stream to my husband's iPad (and Apple ID)?

My husband and I have different Apple ID and iCloud photo stream.

When I take photos on my iPhone, registered to my Apple ID, can I have them automatically uploaded to my husband's iPad 2 registered to his Apple ID?

You could share a photo stream with him. Here's a youtube tutorial on how to set it up.

Apple's solution isn't actually the easiest for this.

Yes, you could share Photo Streams, but you have to push each picture you take to the shared stream. At that point, everyone that subscribes gets all the pictures you have pushed, but you are on the hook to push each picture since you can't just turn on every picture and have them all go to the share.

I would recommend looking into dropbox which is designed to pull all photos and videos taken and place them in the cloud.

Both you and your husband could start with the same dropbox account - and if you didn't want to see his pictures, you could make two dropbox accounts and share your picture folder with his account and he would get all your pictures but you wouldn't get his.

Either way, once you had set up the app and the account(s), you have only to open the dropbox app on your device once you've taken one/multiple pictures and they will start pushing to your private shared storage on Dropbox for your husband to see and use.