How should I punctuate around quotes where the punctuation required by the quote interferes with the punctuation of the sentence?

The American convention in quotations is (typically) to place punctuation inside quoted text. But I always run into situations where the punctuation of the quote interferes with the punctuation of the sentence. How would you punctuate this (American, non technical)?

When my friends ask, "What do you want for your birthday?", I never know how to respond.

It seems odd to place the last comma outside the quote simply because of the question mark. Is that the preferred (i.e. most often accepted) standard?

The British put them outside the quotes, which seems much more logical.

The American style is to put the punctuation inside the quotes. The American version is often known as "Typesetter's Quotes".

As you can see, I go with the British version, at least in informal writing.

Interesting fact: They are called typesetter's quotes because when typesetters were laying out the typesetting blocks putting the small blocks for punctuation inside the quotes made the layout more stable and less prone to shift around. That's probably why it seems so illogical, it was done for mechanical reasons, not linguistic reasons.

Whoever said "The Chicago Manual of Style (6.8) says that When my friends ask, "What do you want for your birthday?," I never know how to respond. is the correct form." was most likely mistaken.

To begin with, they are probably referring to the 15th edition, where section 6.8 addresses periods and commas inside quotation marks, rather than the current 16th edition, where section 6.8 addresses punctuation with URLs and e-mail addresses. However, 15th edition section 6.8 does not address question marks and I could find no example of question-mark followed by comma followed by closing quote in the 15th edition. In any case the 15th edition is out of date.

The current edition (the 16th), forbids the construction of question-mark followed by comma followed by closing quote with one very specific exception. In section 6.119, punctuation that is part of a title is treated as if it is not punctuation, so if the title ends with a question mark, it would still be followed by a comma. However, if what is being quoted is not a title, then the comma is dropped as in these examples from the 16th edition:

“What’s the rush?” she wondered. (section 6.10)

Is it worth the risk? he wondered. (section 6.67)

“Are you a doctor?” asked Mahmoud. (section 6.119)

See all the Chicago Manual of Style Online Q&A where they change/correct

Can you believe that I said, “When she says, ‘Do you know which fruit Jim likes best: apples, bananas, or oranges?,’ tell her this: ‘Actually, I once overheard Jim say, “I only eat pears!” ’.”?!

to

Can you believe that I said, “When she says, ‘Do you know which fruit Jim likes best—apples, bananas, or oranges?’ tell her that, actually, I once overheard Jim say that he only eats pears”?

I find this entire discussion quite intriguing, to be honest. Assuming that most people will come here looking for guidance on a rather non-complex scale:

The American convention for punctuation of quotations is that commas and full stops (aka the '.') always go inside the quotation. This is true. This is to assist with organization, but also to eliminate duplicate sentence-ending punctuation.

In the example given here, it has been my "American convention" understanding since as far back as I can remember, as well as through mutual discussion in the professional realm, that if you are writing a spoken question or exclamation like this, you do not add additional punctuation around the quotation. The only time you use a comma in this structure is if it is a statement. Just remember that, and you should be good. If you're asking a question or exclaiming, you would use the '?' or '!' instead of the comma and continue the sentence.

As for the British conversion of the rule, I think people are getting too deep into the thought process and thus, getting themselves a bit confused. There is not a great deal of variation between American and British styling when it comes to quotation punctuation, generally speaking. There is the inversion of single and double quotes, and the fact that where American rules state to put commas and full stops inside the quotes and British says to place them outside, the rest of it is pretty much the same. Of course, if you want to get really far into the nuance, you could probably find more variation than this, but my experience as an editor that works in both the American and European publishing markets has demonstrated that there isn't a whole lot to be found.

TL;DR? No. Don't put a period or comma outside the quotation marks if you use an exclamation point or question mark to end a quotation. That ending mark within the quotation is sufficient.