You communicate effectively.
Communication skills are some of the most valuable skills a person can have. Oftentimes, when problems in a family or with a relationship arise, it is from a lack of communication or listening. Happy, healthy families are those who communicate effectively. Some of the ways you may do this includes listening to each other. Each family member listens to what the other is saying without interrupting or letting their mind wander. They also try to understand what the other is saying and asks questions if something is unclear.

You fight fair.
All families have squabbles. A healthy, happy family, however, resolves their differences and misunderstandings by talking calmly, avoiding shouting and yelling, and not being accusatory or insulting, even when upset. Fighting fair also includes giving the other person the chance to tell his or her side of the argument without interrupting.

Part of fair fighting includes apologizing when you know you have done something to hurt another member of your family. Healthy, happy families also forgive one another when they are apologized to, so no grudges are held.

You are unselfish.
Happy, healthy families put the needs of each other over their own. If just one person is doing this, then the relationship in the family is one-sided and not happy. However, when everyone is unselfish and tries their best to make each member of the family happy, everyone ends up feeling loved and taken care of.

You respect each other's differences.
Even in a family setting, where each person was raised in the same house with the same values and principles, there will be differences in thoughts and beliefs. As long as the family member isn't doing something that harms themselves or others, these thoughts and beliefs should be respected.

You support each other.
Everyone has different goals, dreams, and aspirations. A healthy, happy family supports each other, even if they don't agree with the dream their family member is pursuing. For example, if one child wants to try out for the basketball team even though she is not very athletic, a happy family is one that would support her in her decision and help her practice, rather than encouraging her to try something else or discouraging her from her goal.
Parents teach their children.
A happy family is one in which the children are not spoiled, bratty, or demanding. One sign of a healthy, happy family is when the parents teach their children to be respectful to adults and to each other. They also don't give in to their children's demands, discipline fairly and consistently, and teach them the value of work; for example, if a child wants a certain toy, instead of buying it for them, the parents might give the child extra chores around the house so they can earn the money and buy it themselves.

Most people would like their family to be a happy, healthy one. If your family does the above things the majority of the time, then you probably have a happy family. The above signs will also help you to know what you can do to make your family happier.