It's "My family and I" if it's the subject: My family and I are going to Paris.It's "my family and me" if it's the direct object: They are visiting my family and me.
Family's are supposed to care and help each other through hard times. They usually care, discuss not argue and never stop loving each other. Good family's never fight and are always loving. Family's...
He and his family--if in the subject position. i.e. He and his family attended the wedding. him and his family--if in the object position. i.e. The food was saved for him and his family.