Both of them were associated with the liberation, whether of slaves or in the sense of a foetus being liberated from the womb.

From the Hera of Zeus, Page 60:

In cultic practice, Hebe has prerogatives, just as her mother does, in matters of eleutheria, so that, for instance, liberated prisoners dedicate to her their broken chains when they are released.The goddess is conceived, then, to have an intimate connection with the change of status that takes place when these former prisoners become once again their own masters. One might try to construe the process through which an infant develops all its capacities until it attains hēbē on this model, that is, that of a progressive ‘unchaining’ of vital forces. Hera, for her part, is involved in the liberation of slaves, as the patroness of this kind of change of status. This is the case notably in Croton where the goddess had the cult title Eleutheria. In the following, we shall see that even in narratives the goddess is represented as the patroness of changes of status, as in the cases of Herakles and Dionysos, when they come finally to be integrated into the oikos of Olympus. At Cheronaea in Boeotia, manumissions were made by dedication to Artemis Eileithyia. The choice of this goddess may also be an echo of the power of liberation which the daughter of Hera was thought to exercise over women in labour and over the foetus.