If your file is to be printed CMYK, try setting your rich black to 40c30m30y100k. That will give you a nice 3/c gray for the black to lay on top of. Can't say if that will totally solve your problem but that's the formula we always use for rich black.
Thanks for the insight. That mix seems to work well. It's odd this problem only happens for me in Indesign. When I do similar effects in Photoshop I dont seem to have that problem.
Applying a rich black is a good idea for going to professional printers. But it's rarely a good idea when printing from a home printer/digital printer.
I find it best to go the Edit> Preferences and in the Appearance of Black change the output to Rich Black.
You can then leave the Black as 100% black in the layout - and output to an RGB device as Rich Black.
NOTE: This only affects RGB devices (regardless of whether it uses CMYK or RGB inks the device is inheritently RGB)
In regards to Photoshop - it's not the same as Indesign, that's why it doesn't behave the same.