Positives
-it may be a very economic solution -not always, though, as sometimes such homes are so big that they are basically separate and the only common room is the kitchen
-the family spends lot of time together
-it can create a great family atmosphere and close relations
-there are less problems with who will take care of small kids if the parents urgently need to leave (no need for a babysitter and useful advices from the older generation regarding bringing up the youngest ones)
-the members of the younger generation might help with shopping or housework the older are not able to do anymore
-on the other hand, the older generation could for instance cook while the young are at work- mutual help is essential
-many older people feel quite lonely - living in the same house as their kids and grandchildren could prevent these feelings; they always have someone to talk to, to spend some time with and so on
Negatives
-lack of privacy, private life, there is always someone there
-too significant interference in each others' lives
-disputes about bringing up the youngest members of the family (parent usually have a feeling that the grandparent are spoiling the kids too much)
-too good relations between children and their parents is not always such a fantastic thing (no woman wants to be compared to the mother of their partner - e.g. "my mom is the best cook in the world")
-having to adjust to more people and respect the needs of more generations - it is quite difficult at times, due to big differences
It is extremely toughto name general good and bad sided of multiple generations homes. It all depends on mutual relationships among the family and strict rules right from the start. Honesty is very important, though. In case you believe living in such a home is definitely not for you, then do not do it. Yes, your parents really want it, but what about you? Ignoring how you feel and your own wishes in the matter is a recipe for disaster.