I'm not able to reproduce this for H1s or H2s on your site, however I can see that you've styled All H3 Headings with
position:absolute, which is what's causing H3s in your blog to appear below the content like that.
If you go to a blog detail page and select one of the H3 headings at the bottom like so, then click to active that "When inside of" style selector, you'll be able to override the All H3 Headings styles used on the front page and set All H3 Headings inside .post-body rich text elements to have
Note: the font-color is currently white but you can see the selection box around the H3 Element in the screenshots
Hope that helps!
The site's looking really great btw!