Alternate Chapter and Section Title in Header

Tex experts,

I am finishing up a book with a publisher, and I was told to alternate chapter and section titles in the header. Below is some LaTex codes I came up with for it. But what I got is having both chapter and section titles in the header on all pages. I use LyX as my LaTex editor. Any help would be greatly appreciated.

usepackage{fancyhdr}
pagestyle{fancy}
fancyhead[LE]{chaptermark}
fancyhead[RO]{sectionmark}