The current version of Juicebox-Pro (v1.5.1) should be fine on an https:// site.
There was previously a problem with the Juicebox logo (in Juicebox-Lite galleries) linking to our website via an http:// link but this was fixed in v1.5.0 (and only ever affected Juicebox-Lite, not Juicebox-Pro, which does not include any branding).
Please check your gallery's XML file to make sure that there are no http:// links in any of the imageURL, thumbURL or linkURL entries.
There should certainly be no trouble with the Juicebox core files so the mixed content is likely to be originating from custom data.
I notice that you are using the Juicebox module for Drupal (an unofficial plugin which was not written by ourselves) and it is the module that generates the XML file.
If the problem is with links in the XML file, then you might need to contact the author of the module in the Drupal forum to ask how this can be resolved.
I hope this points you in the right direction.