I've never a great deal of luck with frames on mobile devices and there are also drawbacks to loading Juicebox galleries into frames (such as the inability to expand galleries beyond the frames) so I'd avoid frames if at all possible.
For other disadvantages of loading Juicebox galleries into iframes, please see the Using an External Gallery Folder support section (scroll down to "2) Using an iframe").
Thankfully, there are several alternatives that you might like to consider.
Suggestion #1
Take a look at the Side Menu Example in the Embedding Multiple Galleries support section.
The web page is laid out using CSS (instead of frames) and the gallery index is housed in a side menu.
In this example, there is a separate web page (including the side menu) for each gallery but you could perhaps use this layout in conjunction with the Switching between Multiple Galleries using JavaScript technique so that there is only ever one web page and the galleries are loaded into a <div> container (similar to targeting an iframe) on demand.
You can view the source of the example pages in your web browser and copy/modify them as required.
Suggestion #2
You might like to take a look at the Juicebox skin for jAlbum.
jAlbum is not free but the program is quite powerful in that you can point it towards an entire directory structure and the program will create a Juicebox gallery for each and every folder in the input, all at once. All galleries will be linked together by a navigation tree in a side menu. The resulting web page does not use frames (or iframes) and also uses the JavaScript baseUrl switching mechanism to load the galleries when the tree nodes (each representing a different gallery) are clicked.
Suggestion #3
Perhaps the easiest and best option for creating a complete portfolio website from scratch would be to use Showkase.
Showkase is a PHP web application which in installed on your web server and whose interface is accessed via a web browser.
Showkase has full support for Juicebox-Pro and the galleries can be created within the application itself via its interface (or created with JuiceboxBuilder-Pro and imported).
You can create Gallery Index pages and have as many galleries listed on each Gallery Index page as you wish.
Each gallery is represented by a thumbnail image with the gallery title displayed below and the gallery is opened when the user clicks on the image.
Demo sites created with Showkase can be found here and a sample Gallery Index page can be found here.
Showkase can also create non-gallery pages (About, Basic and Contact pages) where you can add information about yourself (or any other content you like).
All of this is done automatically within the Showkase interface without the need for any manual coding at all.
You can take a look around the Showkase interface by logging into the Live Demo Admin.
Showkase can be purchased as Showkase-Standard (which comes with Juicebox-Lite) or Showkase-Pro (which comes with Juicebox-Pro).
The only difference between Showkase-Standard and Showkase-Pro is the bundled viewer (Juicebox-Lite vs Juicebox-Pro).
I hope you find this information useful.
If you have any further queries, please let me know.