Breast-feeding can certainly help provide immune protection against multiple illnesses, but not if a mother does not have immunity to a certain disease such as pertussis.
Innate immunity is the defence against infection that babies are born with, as opposed to adaptive immunity which is acquired as people develop antibodies through their exposure to disease-causing agents.
Whereas adaptive immunity is thought to be a response to specific bacteria, viruses, fungi and parasites, innate immunity has always been seen as the body's general response to all threats of disease.
HSE, however, were resistant to plenty of disease-causing agents other than the H. simplex virus, suggesting that innate immunity could be specific, too.