You can insert an axes object spanning this whole figure as a background and use its ButtonDownFcn:
BGcolor = get(0, 'DefaultFigureColor');
BGaxes = axes('Units', 'normalized', 'Position', [0,0,1,1], ...
'XTicks, [], 'YTicks', [], ...
'Color', BGcolor, 'XColor', BGcolor, 'YColor', BGcolor, ...
'ButtonDownFcn', 'disp(''Background'')');
DataAxes = axes('ButtonDownFcn', 'disp(''Data'')';
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