Ok, I think I understand now. You mean that yellow object might actually be a rectangle, underneath everything else? Then transparency isn't exactly what you need. Kind of though.
Since I can't see the whole image, I'm not positive these steps will work. But for what I can see, and how I assume the drawing is made, they should work. If they don't work, we'll need to see the SVG file, so we can know what kind of objects are there.
-- if you have made any Groups, you'll need to ungroup everything
-- if the black lines are strokes, you need to do Path menu > Stroke to Path
-- select all the black objects and do Path menu > Combine (hint, in case you didn't already know - hold Shift key for multiple selection)
-- for every color that you're using, you need this combined black object, so duplicate it as many times as you need (from what I can see, that would be twice)
-- select one color (for example, select that white object) and one of the black duplicates (select them at the same time)
-- Path menu > Difference (that black object will disappear in this operation, that's why you need the other duplicates)
-- repeat for all the other colors
Let us know how it goes
