What does Jem learn about Aunt Alexandra--the good or bad?
Most of the opinions of Aunt Alexandra's behavior in To Kill a Mockingbird come from the eyes of Scout. We do know that
Jem and I viewed Christmas with mixed feelings. The good side was the tree and Uncle Jack Finch... A flip of the coin revealed the uncompromising lineaments of Aunt Alexandra and Francis.
Jem seems to have a slightly higher opinion of Aunt Alexandra than Scout, partly, as Atticus tells his daughter, "Aunt Alexandra didn't understand girls much, she'd never had one." Aunt Alexandra's attitude toward her family heritage
... amused Jem rather than annoyed him: "Aunty better watch out how she talks--scratch most folks in Maycomb and they're kin to us."
Jem aggravates his aunt when he questions the character of their "famous" kin, Joshua St. Clair; later, he shows "disgust" when Atticus tries to defend her beliefs about the "gentle breeding" of the Finch family. Jem makes Scout promise " 'not to antagonize Aunty' " while Atticus is busy preparing for the Tom Robinson trial. Jem's promise to " 'spank you' " leads to a fight. When Alexandra scolds Dill for his " 'cynical' " comments about Aunt Rachel's secret alcoholic consumption, "Jem's eyes flashed at her." Jem defends Scout after Alexandra's refusal to allow Walter Cunningham Jr. to visit the Finch house, arguing with his aunt, but then reminding Scout that
"she's not used to girls like you... Aunty's so hipped on the family because all we've got's background and not a dime to our names."
All in all, Jem's relationship with Alexandra is slightly more distant than with Scout. He seems to care little for her, but since Alexandra spends more time trying to make a lady out of Scout and less time with him, his attitude is just to ignore her. Both Scout and Jem seem to agree about Aunty's best asset: She is a great cook.