This is certainly possible.
Take a look at the View Resizable Gallery with Top Menu Example in the Embedding Multiple Galleries section of the Embedding Guide.
If you view the source of the web page in your browser, you should hopefully see how the example works.
You can then copy and modify the code to suit your needs.
An automated solution would be to create a multiple-gallery album using jAlbum and the Juicebox skin.
When using jAlbum and the Juicebox skin, you can drag and drop a complete folder structure into jAlbum's main window and click 'Make Album'.
The resulting album will have a separate Juicebox gallery for each and every folder/subfolder in your input structure and all the galleries will be linked together via a JavaScript navigation tree (displayed on the left of the screen). On clicking a link for a gallery, the current gallery is replaced with the newly selected one.
Here is a sample album created by jAlbum and the Juicebox Skin.