I do not see any evidence of the characters becoming immature.
link Edward started out as a guy who was afraid to pursue a relationship with Bella. He was generally unhappy and lonely. He had dark thoughts about him own existance.
As he becomes closer to Bella, she helps him realize that he is capable of loving and being sincere. He can protect her instead of put her in direct danger. He is not as evil as he thought. She helped him become lebih confident in his own self control.
Jacob was just a kid in the beginning. He was playful and didn't take much seriously. He wasn't exactly the leader type. While still playful and a jokester in the end, he has become a leader. He always did what he was told in the beginning. He went to Bella's prom under his father's orders. He did whatever Sam told him to do when he joined the pack. He later began to stand up for himself and prove that he could be a leader if he wants to, to the degree where he began leading his own seperate pack.