In Jane Eyre what do Eliza and Georgiana experience at their mother's death?
In Chapter 21 Jane returns to Gateshead to see her dying aunt who has been asking for her. Interestingly this allows the reader ample evidence of how Jane's character has developed in the interim since she left Gateshead all those years ago. Despite the cold and unfriendly greeting she receives from her cousins, Jane is not flustered. She says:
A sneer, however, whether covert or open, had now no longer that power over me it once possessed...
However, to answer your question, at the end of this Chapter, Mrs. Reed dies without either Jane or her daughters present. At the news, Georgiana burst out weeping and said "she dared not go" to look at her mother's corpse, so Jane and Eliza go alone. Note how Eliza responds:
Eliza surveyed her parent calmly. After a silence of some minutes she observed -
"With her constitutinon she should have lived to a good old age: her life was shortened by trouble." And then a spasm constricted her mouth for an instant: as it passed away she turned and left the room, and so did I. Neither of us had dropt a tear.
Remember how Jane summarises the excesses of her two cousins:
Feeling without judgement is a washy draught indeed; but judgement untempered by feeling is too bitter and husky a morsel for human deglutition.
Georgiana, with her obsession on getting married and emotion, represents the dangers of unfettered feeling, whereas Eliza, with her focus on retreating from the world, represents the extreme of judgement. Note that these two opposing forces are acted out in various characters in the novel, though to differing extents, and most importantly, within Jane herself. But to conclude, both sisters show their character in their response to their mother's death - Georgiana shows an excess of feeling, and Eliza an excess of judgement.