It is not possible to incorporate a video within a Juicebox gallery.
As you are aware, Juicebox (as an image viewer) does not support videos (as noted in this FAQ).
The best you could do would be to include links within your gallery to go to separate web pages with your videos embedded into them. You can include links within image titles and image captions using HTML formatting (as noted in this FAQ) or you could use the linkURLs in the gallery's XML file (which can be entered on JuiceboxBuilder-Pro's 'Images' tab) which would be opened when the user clicks on the Open Image button on the gallery's Button Bar.
I realise that many users have requested video support but Juicebox was designed as (and is) an image viewer.
Users are free to suggest whatever they like in the Feature Requests thread but it is up to the developers to decide which suggestions will be taken forward.
An alternative solution might be to include both Juicebox galleries and web pages with videos within an integrated web site.
This can be achieved using another one of our products, Showkase.
Take a look at the Patrick Surace demo gallery on this web page for a web site created with Showkase which features Juicebox galleries and Vimeo videos (on different pages).