There were a few things Neville was jealous of.
He was jealous of Harry's bravery. Every single year Harry proved to everyone how brave he was. He battled Voldemort in his first year and the basilisk in his second. What did Neville do? He earned a few points and fainted in Herbology. Harry took on hundreds of dementors in his third year and won the Triwizard Tournament in his fourth, battling Voldemort again. Neville only revealed to everyone he was afraid of Professor Snape and became terrified in front of the entire classroom just because a little bug was under the Cruciatus curse.
Harry founded an army for Dumbledore and fought Voldemort for the third time in his fifth year and in his sixth year he was at the top of his class in Potions, became the Quidditch Captain for Gryffindor, was a member of the Slugclub and after the sixth year, he left with his friends to fight Voldemort. Neville? Oh, he fought with Harry in the Department of Mysteries, but most people didn't remember that. He was invited to one Slugclub meeting, but didn't get invited at all to the others. Sure, he fought against some Death Eaters at the end of their sixth year, but again, who remembered that?
Neville was also jealous of Harry's strong friendship with Hermione and Ron. Neville frowned every time Harry tried to push his friends away. He said he didn't want to get them into trouble, or that this was something he had to do alone. Neville didn't understand why Harry acted in this way. He would have loved to get that support if he were in Harry's shoes.
It was only in Neville's seventh year when he began to realize how brave he really was. It was pointed out to him by Luna after a mission the DA went on where they wrote slogans on the walls. Several members were almost caught, but due to Neville's quick thinking, everyone managed to flee.
Neville, the plump boy who feared Professor Snape was suddenly the leader of a group that was fighting back during these dark times.
Everyone tried their best to be optimistic during the entire year, but it was difficult. A lot of rage was building up in many students and often did that rage erupt. Most students burst out in classes, yelling at the Carrows about how unfair everything was, pointing out flaws in their logic against Muggles and Muggle-borns or even speaking out against their cruelty. Even a few Slytherins did so, but that was a rare sight.
There was an unspoken rule over what could be talked about and what couldn't in the DA. They tried to avoid what-if questions, such as "what if Harry's dead?" or "what if You-Know-Who actually wins?". Speaking of their missing friends was strictly forbidden. A couple of times did a member start yelling at others about their missing friend, only to break down.
Seamus completely lost it when he was asked by Anthony Goldstein why he spoke so heatedly against the Carrows when they started talking about how disgusting Muggles and mating with Muggles was. He said that Dean was his reason. Neville could tell how much Seamus missed his friend. He had spent a night comforting Seamus as he sobbed into his pillow, praying out loud to God to keep Dean safe.
Zacharias Smith once entered a DA meeting with an angry look on his face. When Susan gently touched his shoulder and said his name, he started yelling all sorts of filthy things about the Carrows, making Hannah frown at his filthy mouth, and only yelled louder when someone else tried to talk. He started to shake once he mentioned Justin Finch-Fletchley's name and he started to curse more, yelling how wrong the Carrows were about Muggle-borns. He left the Room of Requirement after his outburst. The very next day, Zacharias acted like nothing had ever happened.
That brings up another thing Neville was jealous of. He was jealous of Justin Finch-Fletchley. It sounds strange that Neville, a pureblood, was jealous of a Muggle-born who was fighting for his life, but that wasn't what he was jealous of. He was jealous of both Justin's and Ernie's strong friendship with Hannah Abbott.
They had been three best friends since their second year and were often nicknamed as "The Other Golden Trio" or "The Bronze Trio". In Neville's sixth year, he started to notice how beautiful Hannah was. They both took N.E. in Herbology and usually sat together. They became good friends and Neville started to fall for her. She was pulled out of Herbology class one day by Professor Sprout and she didn't return. When Neville heard that her mom had passed away, he was shocked. He did see Hannah once more before she was pulled out of school, sobbing in Ernie's arms while Justin rubbed her back, both whispering something to her.
Even though Justin was gone and Neville had started dating Hannah, she still preferred to be comforted by Ernie rather than Neville. If they received bad news, if Hannah was tortured during detention or if she was just feeling down, she would always seek out Ernie.
That made Neville jealous. He started to consider the fact that Hannah cared more for Ernie than for him. Neville confronted Hannah about this, which she denied, but she couldn't answer why she preferred Ernie's comfort over Neville's. They barely spoke for a week afterwards, which lead to a heated quarrel between Neville and Ernie. After that, Neville tried his best to push back the jealousy that came every time he saw her in his embrace.
After the war had ended, Ernie and Hannah were reunited with Justin, who'd managed to stay hidden from Snatchers. He watched her cry in their embrace and Justin giving both of them a big, fat kiss on their cheek. She was smiling, but when she caught Neville's eye, she beamed. She left her two best friends, who were chatting to Seamus and Dean, and ran to Neville. They embraced and she gave him a soft kiss.
"You are so brave." She whispered in his ear. "I love you so much."
Neville may not be as brave as Harry, but he doesn't need to be. He may not have the same type as friendship Harry shares with Ron and Hermione, but he'd never exchange that for the bonds he made trough the seventh year to Seamus, Ginny and Luna. He will most likely never understand Hannah like Ernie and Justin do, or share the same connection, but he is the one who wakes up next to her every day.
Yes, Neville may be jealous of a few things, but he also appreciates what he's got.