STD and vaccine’s for Expectant mothers?

If the parents of an unborn child have sexually transmitted diseases, wont the child be born with them? I know a couple, where the expectant mother has HPV, (Genital Warts) and the father has Hepatitis C. As far as I know, now that they have transfused body fluids, the expectant mother now also has Hep. C. My question is will the baby be born with the diseases and is there a vaccine once he/she is born to cure it? Does the mother now also have Hep.? And will the baby have hep. and HPV for the rest of it's life?