I have tested the following code and it works. Add it to your own.
% In the pushbutton3 callback
handles.output = hObject;
backgroundImage = importdata('background.jpg');
imshow(backgroundImage, 'Parent',handles.axesBackground);
axis off;
axis image;
guidata(hObject, handles);
% In the pushbutton5 callback
handles.output = hObject;
littleBoxImage = importdata('image.jpg');
imshow(littleBoxImage, 'Parent',handles.axesLittleBox);
axis off;
axis image;
guidata(hObject, handles);
Defining the "parent" property allows you to choose in which axes you will display the image. I had used the axes(handles.myAxes) for plotting, not for image display, so I suppose that was the problem.
This should (finally!) work. Give it a try ;-) .
