My house is not my home

It makes a little sense, but that is not the usual context in which the phrase is used. "My house is not my home" is usually meant to convey that you do not necessarily feel attached or obligated to the place where you physically reside. If I like to travel, for example, I may feel that no single place is my home because I feel at home everywhere. So even if my actual house is in Ohio, I would say "My house is not my home."