Leonard was Sheldon's roommate in The Big Bang Theory for years before he was ready to take the next step and move in with Amy. Due to Sheldon's child-like nature, Leonard and his wife Penny were more than his best friends; they were his parental figures. Sure, the couple got sick of Sheldon's antics and wished they had more time to their selves but at the end of the day, there wasn't anything they wouldn't do for Sheldon.
There have been multiple instances throughout the series where Penny and Leonard acted as Sheldon's mom and dad. They comforted Sheldon after his nightmares, drove him anywhere he needed to go, and prepared him for big life moments. Mary Cooper may have been Sheldon's biological mother, but Penny and Leonard were his Pasadena parents.
When Sheldon Moved Out
In season 10's "The Cohabitation Experimentation," a flood in Amy's apartment encouraged a lifestyle experiment for the couple. Amy and Sheldon would stay in Penny's apartment while Penny and Leonard remained in Apartment 4A. Sheldon was nervous to leave the comforts of home, so Leonard and Penny slowly walked him across the hall to Apartment 4B and saw him off. As soon as it was Sheldon's bedtime, Penny and Leonard threw a dance party for themselves to celebrate being empty-nesters.
Two Christmases
In "The Romance Recalibration," Penny and Leonard go through a rough patch as a married couple. Penny felt like Leonard stopped putting in the effort and that the romance was leaving the relationship. To help his friends (aka mom and dad), Sheldon created a relationship agreement for them.
Before drawing up the contract, Sheldon asked Penny and Leonard, "If you get divorced, do I get two Christmases?" Not only is that something a child would ask their parents but creating a relationship agreement for Leonard and Penny meant saving their relationship, which comforted Sheldon at the same time.
The Trip To Disneyland
When Leonard and Penny broke up in season 3, Sheldon was torn. Was he able to be friends with both of them or would that be inappropriate? After an awkward encounter in the laundry room, Penny and Leonard decided to be civil for the sake of Sheldon, mirroring a conversation two parents would have over their child during a breakup.
In "The Spaghetti Catalyst," Penny took Sheldon to Disneyland and came back later than usual. Leonard acted as a newly single father and was concerned about Sheldon's bedtime and what he ate for dinner. Penny defended her mothering duties and the two sent Sheldon off to bed. It was the perfect example of Sheldon acting as Penny and Leonard's son.
The Comic Book Trip
Sheldon does not handle arguments well. When two people are arguing with each other around him, it brings him back to a dark place in his childhood when his own mom and dad used to bicker.
In one episode, Penny and Leonard were arguing so much that Sheldon ran away from home. The couple acted as concerned parents but knew where he went hiding: the comic book store. They both apologized to Sheldon for arguing and promised to do better. Before Sheldon accepted their apology, he asked them if they would buy him a toy. Penny, of course, agreed and made Leonard buy it for him before going home as a family.
Penny's Parenting Book
In season 11, Penny starts reading a parenting book she found at Howard and Bernadette's house. She wasn't pregnant at the time but she was intrigued by the techniques.
That night, Sheldon was in their apartment venting about his frustrations with Amy. Instead of dismissing Sheldon or changing the subject, Penny used her new parenting techniques on Sheldon... and they worked! Sheldon felt safe and heard. Leonard was amazed by Sheldon's reaction and started using the same techniques. They acted like parents and gave their "son" choices, which Sheldon liked.
Soft Kitty
When Penny and Sheldon became closer, she felt obligated to take care of Sheldon when he was sick. Oddly enough, Leonard, Howard, and Raj were nowhere to be found. It turns out that Sheldon can be incredibly needy when he's sick and Penny fell for the bait.
One night, she's tucking Sheldon into bed and he requests a song: "Soft Kitty." From then on, every time Sheldon was ill, Penny had to sing "Soft Kitty" to him as a mother would to her child.
Leonard Comforting Sheldon
When Sheldon, Howard, and Leonard began working on a project for the US Military, Sheldon promised the military that the project would be done earlier than expected. But when he realized he wasn't as smart as he thought he was, and couldn't do the math, he had a minor breakdown. He tried an energy drink for the first time, which made him feel even worse.
When Sheldon finally told the group that he couldn't deliver what he promised, Leonard comforted him by putting his arm around Sheldon. Instead of pulling away, Sheldon cozied up to Leonard and fell asleep — just as a toddler would.
Babysitting
In "The Bon Voyage Reaction," Leonard goes away at sea for a project, leaving behind Penny and Sheldon. This was a first for the pair of disparate friends, but they got along great. The two acted like a little family. In one scene, Sheldon told Penny that Leonard asked him to take care of Penny while he was gone. This is kind of like when a father leaves and he tells his son to be the "man of the house." Those moments together brought Penny and Sheldon closer.
Nightmares
Sheldon is prone to vivid nightmares and dreams. They're so real to him that he panics when he wakes up. When Leonard was away at sea, it was hard for Sheldon to be alone in the apartment. When he had a nightmare, the ability to sleep felt impossible. He ran across the hall, woke Penny up, and spent the night at her apartment (whether she liked it or not). This moment reminded viewers of a little kid having a nightmare and waking up his mom so that he could sleep in her bed.
Their Family Vacations
Before Sheldon moved in with Amy, his mornings, nights, and weekends were spent with Leonard and Penny. Whatever it was that Leonard and Penny had planned, Sheldon assumed he was invited along. In "The Separation Oscillation," Leonard and Penny were shocked when Sheldon gave them a wedding gift. It was a weekend away in San Francisco. Funny enough, Sheldon told them at the last minute that the trip was for the three of them — just like a family vacation!