Assuming body text, I'd prefer, on the basis of clarity, to use a continuous (expect for line breaks) underline for continuous emphasis, just like with one vs. many weblinks. Keep the concept together.

Then "when" to underline may have some relevance to whether it's broken though, or at least "why" to underline. Because it's not a preferred form of emphasis in type, it's useful for emphasising edits, comment targets, and similar, when it will be dropped from the final version. In this case, I'd break the underline at edit break, and not between words otherwise.

Assuming body text, I'd prefer, on the basis of clarity, to use a continuous (expect for line breaks) underline for continuous emphasis, just like with one vs. many weblinks. Keep the concept together.

The "when" to underline may have some relevance to whether it's broken though, or at least "why" to underline. Because it's not a preferred form of emphasis in type, it's useful for emphasising edits, comment targets, and similar, when it will be dropped from the final version. In this case, I'd break the underline at each edit break, and not between words otherwise.