The second main use of the semicolon is to separate items in a list when one item has its own comma.
For example: My favorite books are Gone With the Wind, Alas, Babylon, and The Bronze Bow.
How many books are in that list? Three? Four? Not sure?
It helps to remember that the purpose of punctuation is to make things clear to your readers. So when one item in a list has its own comma, then you need to show your readers where each item starts and stops. In this case, not everyone knows that Alas, Babylon is the title of a terrific book by Pat Frank about the aftermath of a nuclear war in 1950s central Florida. There very well could be a book titled Alas and a book titled Babylon. You have to make things clear to your readers.
Punctuated correctly, that sentence reads like so: My favorite books are Gone With the Wind; Alas, Babylon; and The Bronze Bow.
Notice that you use a semicolon everywhere you’d use a comma, including the comma before the “and,” which is also known as the Oxford or “serial” comma. I’m a big fan of the serial comma.
I’m all for keeping punctuation to a minimum, or, put another way, I’m for keeping punctuation to the “lowest” level possible. To me, a semicolon is a higher level of punctuation than a comma. I used to think that any sort of internal punctuation in an item in a list would trigger the semicolon rule, but now I don’t. The only way your readers could get confused is if one item has its own comma. An item in a list with a question mark, a colon, or even a semicolon would not confuse a reader; only a comma in an item in a list would cause confusion.