The fate of Superman's parents was revealed on February 12, 1940, with the broadcast of "The Baby from Krypton", first episode of the Superman radio serial. It is quite clear from the broadcast, which you can listen to at the Internet Archive or YouTube, that Jor-El and Lara did not survive the end of Krypton:
So the tiny rocket ship roars into the uncharted heavens as the mighty planet of Krypton explodes into millions of glowing fragments, glittering stars to remain forever in the night sky. Jor-El and Lara, devoted parents of the tiny boy, perish in the giant quake that destroys Krypton.
But what of the rocket ship? Does it reach the earth? Does it find its mark in all the far-flung darkness of space? Remember—don't miss the next installment of Superman!
Batman's status as an orphan was established a few months earlier. According to Wikipedia, Batman's origin story appeared in Detective Comics #33, the November 1939 issue:
The character's origin was revealed in #33 (Nov. 1939), unfolding in a two-page story that establishes the brooding persona of Batman, a character driven by the death of his parents. Written by Finger, it depicts a young Bruce Wayne witnessing his parents' murder at the hands of a mugger. Days later, at their grave, the child vows that "by the spirits of my parents [I will] avenge their deaths by spending the rest of my life warring on all criminals".