If you only need to see the plot from above (2d, xy view), then you can set Z to zero in the surf call but still use your Z for the surface colors. This makes the contour show up above the surface in the z-direction. (If your contour has negative values, use a number smaller (i.e., more negative) than anything in the contour for the surface Z instead of zero.)
X = 1:10;
Y = 1:10;
Z = 10*rand(10);
figure('Position',[1 1 700 1000])
subplot(2,1,1)
colormap(jet)
title('Original');
hold on;
grid on;
surf(X,Y,Z)
shading interp
[C,h] = contour3(X,Y,Z,'k','LineWidth',1);
clabel(C,h,'color','k','labelspacing',60);
colorbar
subplot(2,1,2)
levels = [0:1:15];
figure(1);
colormap(jet)
title('with surface Z = 0');
hold on;
grid on;
surf(X,Y,zeros(size(Z)),Z)
shading interp
[C,h] = contour3(X,Y,Z,'k','LineWidth',1);
clabel(C,h,'color','k','labelspacing',60);
colorbar
