With double knitting, I always try really hard to knit as tightly as I can. The fact that you're moving the yarn from front to back with every stitch tends to make double knitting a lot looser than your normal gauge, and can lead to "show through" if you don't tighten up. I also usually knit on needles at least two and sometimes three sizes smaller than what I'd use if I was doing "normal" one sided knitting.
The only other tihings I can think of is that the black is shedding A LOT,
or that the dye is rubbing through (though that's more common with RED yarn)