Excluding the mental illnesses that are from physical abnormalities in the brain from damage or defect, I would think that someone can "catch" mental illness under the right (or wrong) circumstances.

If an individual grows up in an abusive household and they develop a personality disorder as a result, then they go on to have their own family, I think the people they share a house with could begin to be affected by their disorder to the point of sharing those problems themselves (but without having that original cause).

Mood is contagious, after all, as are outlooks and attitudes. I'm sure everyone has known someone in life who changed after befriending one particular individual. They get drawn into that person's world, and once there, if that friend's world is an unhealthy mental space than I think any mental illness they are experiencing could begin to manifest themselves in the person who was drawn in.

For example, if one person in a household has severe depression, I think that would increase the likelihood of others within the same household developing depression themselves - even if they have not experienced whatever caused the other person's depression. The same goes for paranoia. Group paranoia isn't uncommon, and there are many cases of collective hysteria through the centuries. Cultural beliefs, behaviours, or "magical thinking" gets passed from generation to generation as well. Some of the cultural views, behaviours or delusions can seem more like mental illness than what we call mental illness, yet the people do those things or hold those views because they were passed on to them.

People can also be taught detachment, or become prone to abuse power when others around them do the same. Consider the Nazi concentration camps in WWII. You could definitely make the argument that what the Nazis were doing in those camps could not have come from a "healthy" mind, but do you think they found mentally ill people to man those camps, or do you think that cruelness and sadism grew collectively? I think the Stanford Prison Experiment is a good example of how unhealthy mental states can develop and be spread in previously healthy individuals, and that was only after 7 days. Imagine how much it would affect someone who shares a household with a similar unhealthy mental state, or frequent close proximity.