My site goes through HTTPS, and it says some content is not secure, so when I show unsecured items the HTML page shows up fine.
When in HTTPS though, the page looks incorrectly formatted.
It sounds like your css isn't loading when you're connecting via https.
Is it possible you're not using protocol-relative paths? If your paths are specific to http they won't load when connecting via https:
Replace paths in this format:
<link rel="stylesheet" href="http://example.com/style.css">
with paths in this format
<link rel="stylesheet" href="//example.com/style.css">
See here for more discussion: How to Include CSS and JS files via HTTPS when needed?