So Girl1 has moved beyond the picture book stage (obviously, she being a 2nd grader now).

And I wanted to start making a list of chapter-level books for elementary school students with Asian or bicultural-Asian heroes/heroines.

Here's a few I've found:

Ruby Lu, Brave and True by Lenore Look
Mentions things like having to go to Chinese school on saturdays. Girl1 said it was good.

"From Booklist
Gr. 1-3. Look's Asian American perspective is always like a breath of fresh air in picture books. With Ruby Lu, she ventures for the first time into chapter-book territory, and the results are mixed. Her chapters are oddly disjointed, and the narrative doesn't flow from one chapter into the next. Rather it reads like a collection of nine short stories in which Ruby worries about going to Chinese school (Do they really serve snacks of roasted snakes?), the arrival of a cousin from China whom she's never met, and more. In addition, because the book is billed as the first in a series, Look introduces a load of details to establish character and setting, which threaten to overwhelm what little continuity there is. Still, there's some sparkle here, and Look certainly addresses the need for a recurring Asian American character. A little tightening may give future books the extra punch they need. Terry Glover"

Alvin Ho, Allergic to School, Girls, and Other Scary Things by Lenore Look

Girl1 thought it was cute. I read the first half and thought Alvin's Personal Disaster Kit lists were pretty funny. I also thought there were "insider Asian" references that Girl1 would enjoy getting, like "wasabi-green" cars, etc.

"From Booklist
In the chapter-book universe of Judy Moody and Junie B. Jones it's hard to know what's more surprising about Alvin Ho: his Y chromosome, or his Chinese American heritage. In this book, Look, who has made a career of portraying Chinese American family life in picture books and chapter books, focuses less on cultural commonalities than on the idiosyncracies of Alvin’s family (a dad fond of Shakespearean insults, a grandfather who sews), filling in the Chinese American backdrop exclusively through a small amount of Cantonese vocabulary and some food references. The book’s lighthearted treatment of Alvin’s unusual problem (mutism that kicks in only at school) doesn’t seem entirely apt. Still, many children will sympathize with fearful Alvin, who hates his therapist and marvels at his descent from "farmer-warriors who haven't had a scaredy bone in their bodies since 714 AD." They'll also hope that the book's concluding, unexpected friendship will reap psychological benefits in a sequel. Pham's thickly brushed artwork matches the quirky characterizations stroke for stroke. Grades 2-4. --Jennifer Mattson "

Guess I'll be watching out for Lenore Look.