Put simply, a healthy relationship involves agape love: the true caring about another person without condition. This is surely the case between the devoted father and daughter, Sam and Lucy. However, it's important to note that this kind of love can be found in most any healthy relationship. Using I am Sam as a reference, a healthy relationship can definitely be pitted against an unhealthy relationship. Further, I will prove this to be true by referencing the movie in outline form (as you requested). Let's switch it up a bit, though, by speaking about an unhealthy relationship first.
If there is one aspect of an unhealthy relationship that can be exhibited by Lucy's mother it's neglect! The woman was just looking for a warm place to sleep and took advantage of Sam. After the child was born, she dumped Lucy in Sam's lap and neglected her completely. Although a minor character, the mother must be brought up in regards to an unhealthy relationship.
Now we have to look at the relationship with Rita Harrison and her husband. Rita's husband is a complete cheater. He is never faithful to her and, as such, Sam requests that Rita make a better life for herself. By the end, Rita is brave enough to leave that relationship. Her husband is guilty of the unhealthy quality of betrayal.
Finally, let's talk about the people who bring the case against Sam! Another feature of an unhealthy relationship is obsession. All of these people become obsessed with taking Lucy away from Sam despite the love involved.
This aspect of a healthy relationship can be seen all over the movie. First, of course, there is unconditional love on the part of both Sam and Lucy. Lucy loves her dad despite all of the insults thrown at her by classmates and supposed friends. Sam loves Lucy even though she surpasses his intelligence level. In his own way, Sam talks about the importance of love:
OK, remember when Paul McCartney wrote the song "Michelle" and then he only wrote the first part, Annie said. And then he gave that part to John Lennon, and he wrote the part that said, "I love you, I love you, I love you." And Annie said that it wouldn't have been the same song without that... and that's why the whole world cried when the Beatles broke up on April 10, 1970.
Perhaps most importantly, Lucy says this:
All you need is love.
These are not the only two characters who impart love, however. We must also look at Rita Harrison who has a great depth of love for her son, as we can see many times, but is especially evident at the end of the movie when they go together to the baseball game, mother and son together. There is also a huge amount of filial love between the members of Sam's support group, all of whom have disabilities.
Sam certainly nurtures Lucy in their healthy relationship. First of all, Sam takes ownership of the situation by being the main caregiver of his own daughter. The mother, of course, is guilty of neglect. There are many scenes that are so very warm where both Lucy and Sam learn together, with Sam nurturing Lucy all the way. The one that the title is taken from is when Seuss' Green Eggs and Ham is read. Other scenes that show nurturing is when Sam takes Lucy to buy new shoes or takes Lucy to the park. The irony is that both scenes also show the interference by others.
Sam certainly sets Lucy apart from harm as much as he can (although any parent cannot protect their child from everything) which is also a part of a healthy relationship. Lucy has grown so very nicely, and without much incident, as the movie begins. She has not been put in harms way. She has not been forced on her mother, who didn't want her. She has not been put into the state's care. All of these are evidences of Sam's protection. Even when Sam is fighting for Lucy in court, he is still trying to protect her. I have a vivid memory of the courtroom scene where Sam loses custody and him shouting, "Why isn't Lucy coming home with ME?!?" Further, as a part of his protection, Sam always returns Lucy to the foster parents when she "escapes" to come back to live with him. Even Sam's obedience to follow the law is honorable.
Another aspect of a healthy relationship is the ability to ask for help when needed. First, Sam has a support group of other disabled friends who help each other through life. Second, Sam sets up child care for Lucy when he can't care for her. Third, Sam has the guts to ask Rita Harrison for help when he needs a Lawyer. Finally, and perhaps the most important aspect of support, is the altruism of the foster family willing to help Sam raise Lucy.
Another interesting aspect of a healthy relationship is allowing of the other person's own identity. Sam realizes he is different than his daughter, but he also wants Lucy to live up to her potential and not be burdened by him. Sam even teaches Rita about identity here:
Rita: I just don't know what to call you: retarded, mentally retarded, mentally handicapped, mentally disabled, intellectually handicapped, intellectually disabled, developementally disabled...
Sam: You can call me Sam.