You are almost there.
Try this:
H0=struct('h',[0,0],'Q_centroid',[0,0],'Q_action',[.5,.51,.5,.51],'Q_table',[0]);
H1=struct('h',[0,2],'Q_centroid',[5,0],'Q_action',[.5,1,.5,1],'Q_table',[1;2]);
L0=struct('H0',H0,'H1',H1);
L0Names = fieldnames(L0);
n=numel(L0Names);
stuff = nan(numel(L0Names),2); % preallocation
for i = 1:numel(L0Names)
stuff(i,:) = L0.(L0Names{i}).h; % goes like this: L0.H0.h, L0.H1.h,.... etc
end