No. We are not spirits living in a human body.
There is a continuous mind-matter-process. One mind state following after a previous mind state, at a rapid speed.
Death is just another experience, another mind state which will be followed by another mind state, and so on.
So, there is a continuation after death. Just not a spirit, in the sense you're talking about. What will continue is the mind-matter-process. Or, to quote a monk: "Habits will be reborn."