What an ugly and potentially confusing plotting style. Too bad you are being coerced into doing it that way.
One way to do this is to manually move the plots upward from each other by adding a fixed offset to them (the +2 and +4 you see in my code below), and then kludge the y-axis labels accordingly.
rng default
x = 1:100;
y_H = rand(1,100);
y_M = rand(1,100);
y_L = rand(1,100);
figure
hold on
plot(x,y_H + 4);
plot(x,y_M + 2);
plot(x,y_L);
set(gca,'YTick',0:0.5:5,'YTickLabel',[0 0.5 1 1.5 0 0.5 1 1.5 0 0.5 1])
