How easy is it for parents to get sick from their baby?

Depends. Babies seldom get sick in the first 3m due to immune factors passed over the placenta. After they fade, baby begins to get 5-7 respiratory and 2-4 diarrheal illness/yr that build their own personal immunity. Moms & dads likely likely developed lifelong immunity to many of the germs baby will get new, so they may get some of babies illnesses (colds) but not the ones they have immunity to.