Two commonsense guidelines from The Chicago Manual of Style, sixteenth edition (2010) may be heplful here.
First, with regard to where a question mark goes in a sentence containing an interrogative expression:
6.67 Question mark within a sentence. A question mark is used to mark the end of a direct question within a sentence. ...
[Example:] Is it worth the risk? he wondered.
Second, with regard to the relative weight of the question mark and the period (which is itself a stronger punctuation mark than a semicolon):
6.118 Periods with question marks or explanation points. A period (aside from an abbreviating period [such as the one in etc. or Co.]; see 6.117) never accompanies a question mark or an exclamation point. The latter two marks, being stronger, take precedence over the period. ...
[Example:] Their first question was a hard one: "Who is willing to trade oil for water?"
[Example:] What did she mean when she said, "The foot now wears a different shoe"?
Given that (according to Chicago 6.118) a question mark is a stronger punctuation mark than a period, and that (by general agreement) a period is a stronger punctuation mark than a semicolon, and given that (according to Chicago 6.118) a question mark should always stand alone in a situation where both a question mark and a period might have some claim to appear, it follows that a question mark should always stand alone in a situation where both a question mark and a semicolon might have some claim to appear—as in the sentence
Did you send the revised report[; or ?] I have not seen it.
The question embedded in this sentence ends after the word report; so by Chicago 6.67, a question mark should appear there:
Did you send the revised report? I have not seen it.
Because the following "I" is capitalized, the resulting punctuation looks like two separate sentences—which they effectively are. But suppose that the original sentence had been this:
Did you send the revised report[; or ?] our boss has not seen it.
Here, again, the question mark should displace the semicolon that might otherwise have appeared after report, leaving us for the moment with this:
Did you send the revised report? our boss has not seen it.
But the remainder of the sentence after the question mark is so thoroughly separable from the interrogative part of the sentence that it seems counterproductive to leave the "our" in all lowercase letters. To avoid needlessly halting the reader to ponder whether the lowercase o is simply a typo or reflects some stylistic fancy of the author's, it is better for the writer to accept that the question mark has completely stopped the original sentence in its tracks and to pick up on the next thought in a new sentence:
Did you send the revised report? Our boss has not seen it.