Being disease free is certainly a contributor to happiness but probably not the primary one.  Consider the difference between two communities - one consists of people who are out of work and living in poverty because their main employment source has been closed and even moving somewhere else takes money they don't have.

The other community is a cohesive community where people work together on common projects that support the community and where people have friends and neighbors that they can turn to for support if they need it.  Which community do you think has the most happy people?  Research data shows that health disparities are strongly associated with income inequality.  Social cohesion is positively associated with health.

I agree with Sarah. The notion of a disease free existence is an ideal that would contribute to happiness, but there are so many more factors involved that also contribute. As Sarah suggested, positive interaction with others, love and support, along with a sense of achievement, satisfaction, gratification, a lack of worry and so many other things that - added together - lead to a sense of well being. 

Some people are not disease-free, but happy, while others have comparatively good health, but maybe have less happiness.

This is of course a theoretical question. I agree with the other colleagues. Absence of disease is not a sole determinant or even the major determinant of happiness. Indeed it is not even a definition of health and wellbeing. Equally many people with short and long term diseases with varying levels of severity are happy. Happiness is fundamentally about having something meaningful to do, having people to love, being safe, being valued and so on. Illness can disrupt these determinants of happiness but it need not.