With 10.1

You didn't provide the data so free format:

ListLinePlot[
 Table[{Sin[x], RandomReal[{0.2, 0.4}] + Sin[x], 
    Sin[x] - RandomReal[{0.2, 0.4}], 2 Sin[2 x], 
    RandomReal[{0.2, 0.4}] + 2 Sin[2 x], 
    2 Sin[2 x] - RandomReal[{0.2, 0.4}], Sin[3 x], 
    RandomReal[{0.2, 0.4}] + Sin[3 x], 
    Sin[3 x] - RandomReal[{0.2, 0.4}]}, {x, 0, 2 Pi, 
    0.01}]\[Transpose], 
 Filling -> {1 -> {{2}, Directive[Opacity[0.2], Green]}, 
   1 -> {{3}, Directive[Opacity[0.2], Green]}, 
   4 -> {{5}, Directive[Opacity[0.1], Red]}, 
   4 -> {{6}, Directive[Opacity[0.1], Red]}, 
   7 -> {{8}, Directive[Opacity[0.2], Green]}, 
   7 -> {{9}, Directive[Opacity[0.2], Green]}, 
   10 -> {{11}, Directive[Opacity[0.1], Red]}, 
   10 -> {{12}, Directive[Opacity[0.1], Red]}}, 
 PlotStyle -> {{Darker[Green], Thickness[0.004]}, Transparent, 
   Transparent, {Red, Thickness[0.004]}, Transparent, 
   Transparent, {Darker[Green], Thickness[0.004], Dashed}, 
   Transparent, Transparent, {Red, Thickness[0.004], Dashed}, 
   Transparent, Transparent}, FrameTicks -> All, 
 Frame -> {{True, None}, {True, None}}, Axes -> False, 
 TicksStyle -> Thick, FrameStyle -> Thick]

seems to work but I didn't use FrameTicks