Good question. I often ponder this very subject.
Well, let's start by defining terms:
good
ɡo͝od/
adjective
- 1.
to be desired or approved of.
"we live at peace with each other, which is good"
- 2.
having the qualities required for a particular role.
"the schools here are good"
noun
- 1.
that which is morally right; righteousness.
"a mysterious balance of good and evil"
- 2.
benefit or advantage to someone or something.
"he convinces his father to use his genius for the good of mankind"
re·la·tion·ship
rəˈlāSH(ə)nˌSHip/
noun
1
- the way in which two or more concepts, objects, or people are connected, or the state of being connected. "the study will assess the relationship between unemployment and political attitudes"
2
- the state of being connected by blood or marriage.
"they can trace their relationship to a common ancestor"
3
- the way in which two or more people or organizations regard and behave toward each other. "the landlord–tenant relationship"
So...thinking about it logically from multiple standpoints in our definitions:
A 'good relationship' would be a mutually desired or approved of connection or state of being between two things (people in our case) possessing the qualities for a particular role that is both righteous and advantageous (of mutual benefit) in the way those two things regard and behave toward each other.
~Now, you used the word 'healthy', so :
Simple Definition of healthy
: having good health : not sick or injured
: showing good health
: good for your health
Full Definition of healthy
health·i·erhealth·i·est
: enjoying health and vigor of body, mind, or spirit : well
: evincing health <a healthy complexion>
: conducive to health <walk three miles every day … a beastly bore, but healthy — G. S. Patton>
a : prosperous, flourishing
b : not small or feeble : considerable
So...then by replacing terms:
A 'healthy relationship' is a state of being or connection between two things (in our case, people) that is not sick or injured, conducive to the vigor of body, mind, and/or spirit, and prosperous or flourishing in strength as opposed to being small or feeble.
Thus, based on these definitions and terms, one can surmise that a "good and healthy relationship" would be the culmination of our statements for both a 'good relationship' and a 'healthy relationship'.