To get the fine control over the graphics, I would one probably has to construct each element and combine them. As @Silvia@Silvia points out, exclusions cause separate polygons to be created. When rendered on a discrete screen, these may overlap or have gaps.
That means drawing the step curve and its filling separately, like this:
Plot[Sign[Sin[x]] Ceiling[Abs[Sin[x]], 1/3], {x, -2 Pi, 2 Pi},
PlotStyle -> Red],
Plot[Sign[Sin[x]] Ceiling[Abs[Sin[x]], 1/3], {x, -2 Pi, 2 Pi},
PlotStyle -> None, Filling -> Axis,
FillingStyle -> Directive[Opacity[0.2], Red], Exclusions -> None]
If you don't want to copy, paste, and edit each step function plot, you could write a function to combine both plots, such as the following:
SetAttributes[plotWithFilling, HoldAll];
plotWithFilling[Plot[f_, x_, opts___], col_] :=
Show[
Plot[f, x, PlotStyle -> col, opts],
Plot[f, x, PlotStyle -> None, Filling -> Axis,
FillingStyle -> Directive[Opacity[0.2], col], Exclusions -> None, opts]];
Usage:
Show[
Plot[Sin[x], {x, -2 Pi, 2 Pi}, PlotStyle -> Blue],
plotWithFilling[
Plot[Sign[Sin[x]] Ceiling[Abs[Sin[x]], 1/3], {x, -2 Pi, 2 Pi}],
Red
],
plotWithFilling[
Plot[Sign[Sin[x]] Floor[Abs[Sin[x]], 1/3], {x, -2 Pi, 2 Pi}],
Green
],
AspectRatio -> 1/Pi, Frame -> False]
