You can use the fill function to achieve this.
To do so, first generate the data:
t = datetime(2014,6,28) + caldays(1:10);
y = rand(1,10);
Generate the limits for the black patches:
x1 = datetime(2014,6,30);
x2 = datetime(2014,6,31);
x3 = datetime(2014,7,4);
x4 = datetime(2014,7,5);
Generate some y-values for the black areas
y1 = [0 1 1 0];
Create the axes and create the black areas.
ax = axes;
fill([x1 x1 x2 x2],y1,'k');
hold on;
fill([x3 x3 x4 x4],y1,'k');
Plot the line such that it's rendered over the black areas.
plot(t,y,'y','LineWidth',2);
hold off;
Turn the axes color to red so that it's red for all other areas (per your requirement).
ax.Color = 'r';
The axes also show a changed display for the time.
