Yes, this show had quite a few of these.
* From the theme song: "Mama had a chicken / Mama had a cow / Dad was proud / He didn't care how". As weird as the circumstances are, the fact that their father was willing to accept them as his children without a problem is pretty sweet.
* Just about every time that Cow rescues Chicken or whenever Chicken helps Cow. As much as they clash, the two of them have a very strong bond.
* "The Day I Was Born" has Cow asking her parents, her teacher, and the guy who delivered her (The Red Guy, of course) about the titular day. The Red Guy's story is what truly makes it heartwarming where baby Cow calls out for her big brother and baby Chicken asks to hold her. It's very adorable, especially with how Chicken is normally reluctant to show affection toward his sister.
* The end of "A Couple of Skating Fools." After Cow steps in to help Chicken win when Earl breaks his knee, Chicken gives Earl the flowers and they all have a group hug. They even include Flem and Hiney (The Red Guy's female disguise) in the group hug despite the latter causing Earl's injury.
* "Cow's A Beauty" has the bovine herself attend a beauty contest where she seems outclassed but not only are the contestants civil, two of them even kiss Cow on the cheek when she wins because of her overwhelming charm and inner beauty. And then she shares her flowers with The Red Guy to add more fuel to the heartwarming fire. Chicken applauds his sister's noble gesture.
* "Journey to the Center of Cow" gives The Red Guy a big one. It's one of the few episodes where he plays a completely Protagonist role (as their pediatrician) and makes a genuine effort to save Chicken after he gets trapped in Cow's stomach. Even when he's told only him or Chicken can get out safely, he doesn't even hesitate to tell Chicken to free himself. Outside of calling the parents "Simpletons" (which in all honesty, the question they had asked WARRANTED it!), he doesn't do ANYTHING even remotely evil.
* The episode "Which Came First" revolves around Chicken finding out he's laid an egg ([[spoiler:actually a prank from the Red Guy]]) and having to embrace femininity and motherhood. Despite the HilarityEnsues of the event, the family actually handles the concept in a respectful way:
** Chicken is actually willing about being a girl and mother, for a generally surly adolescent. He refuses to leave the egg except on special events, and takes good care of the egg 24/7.
** Mom and Dad, while generally bonkers, actually show some responsibility and maturity: Mom tells Chicken to head to school and to be a good single mother/student, while Dad cross-questions Flem and Earl on their planned date with Chicken, wanting no funny business with his kid.
** When the egg finally hatches, Chicken screams for his family to come, and everyone is overjoyed about the event. Cow screams that she's going to be an aunty, and Mom hollers for Dad to get the video camera.
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