These typographical devices mean the same thing; therefore, it would be unusual to use both within the same text and it would certainly be unwise to italicize an underlined word.
The titles of these shorter pieces would be surrounded with double quotation marks.
In writing the titles of newspapers, do not italicize the word the, even when it is part of the title (the New York Times), and do not italicize the name of the city in which the newspaper is published unless that name is part of the title: the Hartford Courant, but the London Times.
Here is a formula we recommend: Put the title of an entire composition in italics.
Put the title of a short work—one that is or could be part of a larger undertaking—in quotation marks.