One of the often overlooked points of the story of the Exodus, is the special relationship of brotherly love between Moshe Rabbeinu and Aaron. While sibling rivalry is a common phenomenon and is motivated by jealousy, Aaron showed only love and devotion to his brother, Moshe.
We learn this from Hashem's dialogue with Moshe and the choice of Aaron to be Moshe's spokesman. Hashem tells Moshe, וראך ושמח בליבו. Aaron will rejoice and show gladness in his heart.
Even though Moshe was chosen to be the leader, Aaron was genuinely happy for his younger brother.
When we use the expression איש אחד בלב אחד, one man, one heart, we are referring to that special brotherly love between Moshe and Aaron. We are supposed to learn from this relationship, to remove all jealousy from our hearts.