Yes, it's true that our H is not very aspirated, I totally agree with You Jun examples.
There are muted H and aspirated H, both sound like they are muted, still the aspirated H is slightly aspirated anyway.
But the difference is generally made in the usage of 'liaisons' instead (linkings).
With aspirated we will have le la, with muted h, it will become l' : le héros (aspiré) / l'héroïne (muet)
With un, une there is liaison with the n, but with aspirated h, there is a pause or a long sound for une_ : un habit (un-na-bi) / un haricot (un-a-ri-co) / une habitude (u-na-bi-tude) / une hauteur (u-neu-o-teur)
So I guess our pronounciation of H in chinese words may appear very flat to chinese ears, but we have nice R and U for you to enjoy :-)