You could use findobj() on each figure to find the handles of the two lines. You can differentiate the lines by their LineStyles (maybe there's a better way to distinguish the two lines, but I couldn't come up with it). All together, something like this:
% for final product:
f = figure; ax = axes(f, 'NextPlot', 'add');
filenames = {'file1.fig', 'file2.fig', ..};
for i = 1:numel(filenames)
f1 = openfig(filenames{i}); % load the old figure
lh = findobj(f1, 'Type', 'Line', 'LineStyle', '-'); % find the line with '-' linestyle
copyobj(lh, ax); % copy that line to your new axes
delete(f1); % delete the old figure
end
