We have seen anecdotal evidence of this in our practice. The most unstable parents seem to have the sickest kids. The young son of a divorced friend of mine with a certifiable ex-wife, would come back from his weekends with mother dearest with headaches, stomaches and colds. He would recover over the next week and a half and get sick after being with his mom. It was an obvious cycle everyone was helpless to interrupt.
Now, there is scientific evidence that the phenomena of stressed parents creating sick kids is, in fact, real:
A core principle in the some of the alternative therapies that I use is that in infants you treat the mother not the child. And certainly, when the children are getting sick because the parents are nervous wrecks, the solution is to go to the root of the problem--helping the parents learn coping skills.
A University of Rochester study, reported by New Scientist, found sickness levels were higher in children of anxious or depressed parents.
It also found links between stress and immune system activity in the children.
Unfortunately, many parents are not interested in resolving their own issues when it comes to stress management. They teach their kids by their example in two ways: by externalizing their discomfort and by somatisizing their discomfort, that is by failing to adequately communicate their issues and so have their issues reside in their tissues. This isn't hocus pocus. Children are very good at reflecting and absorbing their surrounding environment. Their most influential environment is the home their parents create.