Headers-Containing-Phrasal-Elements-Break Bug

The following markup:

<H4>Header <EM>Emphasis</EM> Header</H4>

Causes the following:

Header Emphasis Header

It should just have a single line of text. I believe the parser is assuming that the EM ends the H4. This happens with all kinds of phrasal elements, not just EM. For example, A has the same problem.

Bugzilla: Bug 2953