Mental health is always assessed through the lens of cultural norms. Where I am (in Sweden) feeling jealous and acting on it is the cultural norm [1]. (Personally I agree with the GP though and see my own culture as sick.)
A mentally healthy person is content to live their own life, is honest, and doesn't hurt people around them.
Negative emotions aren't necessarily an indicator of mental unhealthiness; resentment, disgust, rage, anger, etc. are all healthy responses to the right set of circumstances. However, when these feelings are experienced when there's no danger, deceit, harm, or violation of a bargain or relationship, it implies an inability of the person experiencing the feelings to be content with their own life, and a desire for goodness to go out of the world (I'd rather you not be excellent at all then have to sit here and compare myself to your excellence).
What's your definition of mentally healthy, then?