AFAIK, your problem is that you don't know, because you're not working in CV (code view) where you are actually inserting the image, and the page-break. If you've inserted the cover INSIDE the header tags, yeah, when you "break" that page, the cover will suck that header right along with it, because they're all (break, cover, header) in the same paragraph. Sigil is doing what it should.
Just turn on CV so you can see what you're doing. Then it's simple. No reason for sturm und drang; if you work in BV, it's like working in bloody Word--you can't see what you're doing, so of course stuff will get bollixed up.