The man of the house would get the privilege of the nice clean bath water. Then all other sons and men, then the women and finally the children. Last of all the babies. By then the water was pretty thick. Thus, the saying, "don't throw the baby out with the bath water," it was so dirty you could actually lose someone in it.
Does throw the baby with the bathwater refer to reused wash water that was so dark one could lose a baby in it? Is it Elizabethan in origin? The phrase in question does happen to date to the 1500s, but to Germany not to England. The rest of the story about babies and bathwater is pure fiction.
Throw the baby out with the bathwater or more accurately, das Kind mit dem Bade ausschutten, is a German proverb that dates to 1512. It was first record by Thomas Murner in his satire Narrenbeschworung (Appeal to Fools) in which he used it as a chapter title. Murner uses the phase several times in the chapter. The original manuscript even has a woodcut of a woman tossing a baby out with the waste water.
The Phrase didn't appear in English for several more centuries, not until Thomas Carlyle translated it and used it in an 1849 essay on slavery: using it as a call to not let the slave suffer in the fight to rid the world of the evil of slavery.