When a person is healthy, he/she is in a state of complete physical, mental and social well being. He /She can perform well physically, mentally, emotionally and socially.
Disease-free simply means that the person is not suffering from a disease or infection. But a person can be disease free, but at the same time in poor health. For example - A person may not be suffering from a disease (i.e. disease free), but may be mentally depressed due to some reason, due to which he may not be able to carry out his social functions. So he is now in poor health (i.e.not healthy).