Fountain of Knowledge

I've encountered similar issues, and I wish there was a hard fast answer for it, but a lot of it comes down to preference - writer and reader.

The way I like to do it is as you described - put one of the narratives in italics. I would also recommend, however, not putting them in the same chapter unless they're both brief snippets that go back and forth. If they are (like you do a couple paragraphs in first person and then a couple in third and switch back) stick with just italics. If you do pages of one (for instance the third person), then even if you only do a couple paragraphs of the next before you switch back, make them different chapters.

I hope that helps a little. Now I'm curious to see what you're working on