There are many recurring "inside-jokes" between Julie and Maddie ("Kiss Me, Hardy!" ohgoshnowi'msadagain), and one of their common discussion topics is listing their fears. Both of them say that they have a fear of growing old, and both of them look back on this in the narrative and reflect on how petty that was, as well as their newer, more "realistic" fears. However, *spoiler oops* this theme of staying young forever is literally achieved at the end of the novel when Julie dies, and she is forever immortalized and can no longer grow old.
Going along with the theme of children never growing up, there is also the parallel between Julie's mother and Mrs. Darling. Maddie jokes about this similarity and the connection between the two mothers seems superficial and mainly based on the girls' mentioning of Peter Pan, but when analyzed the similarities become a bit clearer. Both of these women have lost their children that flew away (Julie and Jamie in WW2 military aricraft and the Darlings via pixie dust), and it is mentioned in the novel that Julie's mother would leave their bedroom windows open at Castle Craig in case they ever flew back in through the window.
Flying is obviously quite prevalent in Code Name Verity, and so is the theme mentioned previously about children's desires to fly. Wendy is disenchanted with her life at home and the impending responsibilities of adulthood, and so she jumps at the chance to go on an adventure with a mysterious flying boy who never grows up. Maddie is portrayed to be much more naive and imaginative than Julie, and the second she sees Dympna crash her Puss Moth in a field she is dead-set on learning to fly. Flying gives the characters in both novels freedom, and as it is mentioned in How to Read Lit Like a Professor, flying is often a symbol of freedom.
There are also parallels between Jamie and Peter Pan, the Glaswegian refugees and the Lost Boys, and most likely von Linden and Captain Hook.