No, people don’t just forget about H and move on.
And yes you can still have babies. There is a chance that you can pass it to your child, but it’s very slim unless you have an outbreak while giving birth, or you are having your first outbreak during pregnancy. If so, your doctor would probably resort to a C section.
Using a condom is the best way to protect him from this, other than not having sex at all. You have told him that you have this disease, and he’s accepted the risks. There’s really nothing else you can do to protect him. Just always avoid sex during an outbreak, as wel