WP Thickbox - use the same template for Inline-Images and IFrame-Content

I am developing a WP-site with mixed Image/Video-content. I want to display them in the WP-core "Thickbox", which works okay.

However, opening an inline-image in the Thickbox triggers a different DOM for the Thickbox than opening an iframe-Content (f.e. Youtube-Videos).

Is there a way I can tell Thickbox which Template to use? I cannot find much documentation about it, even though it's used so much...