They look exactly like their son except Henry has a brown mustache and fuzzy eyebrows, and Courage's mother has eyelashes, gray ears, red lipstick, a blue purse, a yellow hat with a flower in it and a pair of yellow high-heel shoes.
Courage's parents are two caring pink dogs who took Courage to the vet after an accident while playing fetch. However, the Cruel Veterinarian put them in a rocket ship and shot them into space as part of his insane experiment to turn earth dogs into super space dogs.
He attempted to capture Courage too, but he escaped and tried to free his parents though was knocked into the garbage chute, watching his parents shoot off into space forever, upset that he couldn't save them.
Many years later, Muriel took Courage to this very same vet, despite Courage's protests and he (along with Muriel and Eustace) almost ended up suffering the same fate as his parents, but he was able to overcome his past fears, thwart the Cruel Veterinarian, save his owners and lock him up in his rocket. After 5 seconds to launch, the rocket engines under it (off-screen) then ignites and the rocket launches, sending him into space instead and ironically suffering the same fate as his parents.
The Cruel Veterinarian then ended up on the planet where he had sent all his canine patients to over the years, as his insane experiment to turn earth dogs into super space dogs failed (as a result of Courage locking him up inside his rocket), and luckily they were all still alive and well and none of them were pleased to see him, including Courage's parents who then proceeded to maul the Cruel Vet off-screen as revenge.