What if you got white ones and painted them black? I think it would look nice.

Have you checked on Houzz.com for images of your black and white scheme?

Thanks for your opinion smcoxl. I think that may be the way to go as I've checked on Houzz (thanks for the suggestion enduring) and haven't seen one sample (which probably tells me something!)

Not exactly what you are looking for, but might help you visualize...

Oops, thought this was white, but it's silver.
{{gwi:1412016}}

{{gwi:1412017}}

Have you found any medicine cabinets that are mirrored all the way around?

[contemporary bathroom design[(https://www.houzz.com/photos/contemporary-bathroom-ideas-phbr1-bp~t_712~s_2103) by other metros interior designer Atmosphere Interior Design Inc.

Black and white can look really great together. Although my situation isn't exactly the same, I used black and white in a bathoorm. You can check out pics here; maybe it will help you visualize what black and white look like together...

Here is a link that might be useful: Link to home dec post

Thanks very much aa62579, the first picture really does help me to visualize that maybe it will look okay.
Andreadeg, thanks for the link to your bathroom. So nice! I think your white-framed mirror looks great with the black vanity.