'public_html' is the name given to the folder on your web server that represents your root directory.
As an example, if you were to upload a file named 'page.html' to your 'public_html' folder, then you'd be able to see the page by visiting http://alpinedescents.com/page.html
The folder name 'public_html' should not be included in any URLs.
With this in mind, the following should work fine:

<!--START JUICEBOX EMBED-->
<script src="http://www.alpinedescents.com/gallery/jbcore/juicebox.js"></script>
<script>
    new juicebox({
        containerId: "juicebox-container",
        baseUrl: 'http://www.alpinedescents.com/gallery/',
        galleryWidth: "100%",
        galleryHeight: "100%",
        backgroundColor: "rgba(34,34,34,1)"
    });
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

Incidentally, I notice that you can visit your website using either alpinedescents.com or www.alpinedescents.com. However, if you hardcode paths using 'www' in your embedding code, then the gallery will display only when visiting www.alpinedescents.com (but not when visiting alpinedescents.com).
Please see this FAQ:
My gallery works on 'www.example.com' but not on 'example.com' (or vice versa). Why?

Therefore, I'd recommend that you use relative paths within your embedding code and your gallery will then display on both alpinedescents.com and www.alpinedescents.com.

<!--START JUICEBOX EMBED-->
<script src="/gallery/jbcore/juicebox.js"></script>
<script>
    new juicebox({
        containerId: "juicebox-container",
        baseUrl: '/gallery/',
        galleryWidth: "100%",
        galleryHeight: "100%",
        backgroundColor: "rgba(34,34,34,1)"
    });
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

The leading slashes in the paths above denote your root directory so the code will work in any web page throughout your site without modification.

For any other users reading this thread and embedding galleries in Adobe Muse, the following two links may be useful.
Embedding With Adobe Muse: http://www.juicebox.net/support/embeddi … adobe-muse
Alternate Adobe Muse Embedding Instructions: http://www.muse-themes.com/blogs/news/6 … adobe-muse