Applying transparency only to the non-transparent parts of a png

I have a transparent png that has a black and white monochrome illustration in its centre. I'd like to make the monochrome illustration take on a colour in InDesign by assigning a colour to the frame. Is there any way to do this without having to make edits to the image in Photoshop?

I imagine the trick is playing with transparency modes in with the Effects panel--but no luck I could figure out. Typically when I want to do this to a black and white image, I'll give the image frame a fill, and then double click to make only the graphic take on transparency of the background fill. But in this instance, I'd like for the illustration to still take on the Lighten transparency, but for the transparent background to ignore it. I'm trying to achieve a look of a coloured block sitting atop of the background image. Shown below.