Can someone who is pregnant and was diagnosed with hepatitis b have a normal, healthy baby?

Absolutely. The chance of passing the virus to the newborn is extremely small if the baby receives the appropriate vaccinations at birth.
Yes. Recommendations for an infant born to a hepatitis b positive mother include a Hepatitis B Vaccine shortly after delivery along with a dose of Hepatitis B Immune Globulin given at the same time in a different site. Then the child should finish the hepatitis b immunization series. If you follow those guidelines, the child should be okay.