If you turn on window opacity slightly, then background opacity will be factored in. Note a cell's background is mixed with the notebook's. Note that
"Input" cells have a translucent
LightBlue background, RGBColor[0.87, 0.94, 1, 0.6], that appears purplish.
WindowOpacity -> 0.9999, (* something slightly less than 1 *)
Background -> Hue[0.95, 0.8, 1, 0.8]]
There is still a slight problem. It may be hard to see, but the input labels have a rectangle with a slight different color than the window background. It seems that it inherits the window background, and when the two are composited, the result is less translucent. This seems to be an issue whenever translucent backgrounds overlap. Since the OP seems interested only in cells with opaque background, this shouldn't be an issue except for the In/Out labels.
To fix the labels, edit the stylesheet. Enter the style name CellLabel and hit return. With the Options Inspector, change the backgrounds for both Cell Options > Display Options > Background and Formatting Options > Font Options > Background to have 0 opacity, with something like
RGBColor[0, 0, 0, 0]
(Just add the fourth entry 0; the others don't matter. For reasons I didn't track down, once the color was the notebook background, and once it was near white.)