A recurring gag in both of these episodes is that Papa is allergic to so many different things and even to some basic ideas and concepts, such as heights and the idea of Junior failing. Some of the things he is allergic to include: marshmallows, deep pits, and animal fur. While he does act before he thinks, he tries to be a good father to Junior and mate to Mama, despite his goofy antics. Like Pooh Bear, he has a particular love for honey (a common trait shared among heffalumps and Pooh bears), to the point where the mere sight of it is enough to cause his feet to move up and down uncontrollably (he describes this as his "honey feet"). He also has certain abilities that he puts to good use, like the ability to retain huge amounts of water at one time, and the ability to climb trees very quickly.
Papa, his wife Mama, and his son Junior all live in the Hundred Acre Wood in a quaint little wooden house. In "There's No Camp Like Home", they find that someone has taken all of the wood that is their house. Papa immediately goes to find it, only to discover that his home was being used as firewood for Pooh, Tigger, and Piglet's campfire. After Piglet and Tigger see him, they are both scared stiff. When Papa and Tigger get into a small argument about whom the firewood belongs to, they realize that Piglet and Papa 's son, Junior, are stuck up a tree and unable to get down. Pooh comes up with the idea to use Mama's trunk to catapult Pooh up to the top of the tree to get them down. When they succeed, they all go back to Piglet's house to toast marshmallows, which causes Papa to release a very powerful sneeze. At the end of this episode, Pooh, Tigger, and Piglet are on good terms with the Heffalump Family and remain so.
In "Trap as Trap Can", Papa and Junior go out into the forest to practice the 'T 'n' T's', the strategy they use in hunting woodland creatures. Because Junior is struggling, he leaves Papa to cry by himself, which leads to him wondering away with Pooh and Piglet, who welcome him. When Papa realizes that Junior has disappeared, he assumes he has been kidnapped and runs off to find him. As Junior is meeting Rabbit, who is surprised to find a heffalump in his home, Papa sneezes himself into his home and is soon covered in flour as he carries Junior off. As Junior goes back and forth from Papa to Pooh and Piglet, Junior eventually meets Gopher who introduces him to TNT. This leads to Junior feeling upset over the idea of him letting Papa down. Gopher soon comes up with the idea to make it look like Junior has tracked and trapped Pooh and Piglet, and present them to Papa. When Papa sees Pooh and Piglet, they appear familiar to them (seeing as they had met in "There's No Camp Like Home"), but thinks nothing of it and attempts to cage them. When Junior cages him instead, Papa is impressed and tells him to go home and show this to Mama. As Papa waves goodbye to Pooh and Piglet, he releases one last grand sneeze after he realizes that he is allergic to furry woodland creatures like Pooh and Piglet.
Though Junior tells Pooh and Piglet that he would return after "Trap as Trap Can", neither he nor his parents come back for a third appearance (or a second appearance in Mama's case).
Even though Papa got to know Pooh and Piglet in "There's No Camp Like Home", he acts as if he does not know them here (though he admits that they look familiar). This could be because while Papa's family is on good terms with them, it may have just slipped his mind, due to his not-very-intelligent mindset.