Your wife and children will want to be tested and vaccinated, if they have not been already. I'm so sorry you have Hep B. I can tell you are very concerned.
Here is the best answer to "how is Hep B spread", from the CDC. Big Hugs
How is it spread?
Hepatitis B is usually spread when blood, semen, or other body fluids from a person with the Hepatitis B virus enter the body of someone who is not infected. The virus is very infectious and is transmitted easily through breaks in the skin or mucus membranes (nose, mouth, eyes and other soft tissues). This can happen through:
■ Sexual contact with an infected person
■ Direct contact with infected or contaminated blood, even in tiny amounts too small to see
■ Sharing personal items, such as toothbrushes, razors, syringes, or glucose monitors that have even microscopic amounts of blood on them
■ Direct contact with open sores of an infected person
■ An infected mother passing it to her baby at birth
Hepatitis B is not spread through sneezing, coughing, hugging, or breastfeeding. Although the virus can be found in saliva, it is not believed to be spread through kissing or sharing utensils.
Wife of themister, a fine man living with ESLD. Transplant list-2013
“Out of suffering have emerged the strongest souls; the most massive characters are seared with scars.” Kahlil Gibran