Does China even have H-bombs? I was under the impression that they had at most a few dozen fission bombs, more powerful than the ones dropped on Hiroshima and Nagasaki but far weaker than the fusion bombs we have. The kinds of bombs they have would cripple a large city, but not destroy it. If they got a few hits they could hurt us, but not enough to put us in a worse position than them, because you can bet we would unload on them if the used nuclear weapons on our cities, and each one of ours could flatten a 10 mile radius around ground zero and set fires 50 miles away.
I think if we did go to war with China they would not risk using their nuclear armament on us, it would be suicide. Their nukes are probably intended for intimidating their neighbors like India, South Korea, and the above-mentioned Taiwan.