Is there a way for a patient to work with both a chinese and western medical doctor at the same time?

Yes. More western medical doctors are receiving training in integrative and holistic medicine and may be knowledgeable about and therefore more comfortable with collaborating with healers of other traditions. The university of arizona integrative fellowship is one such training program for mds another resource is the american board of integrative and holistic medicine.
Yes. Yes, ideally the 2 should collaborate for your best benefit. I know many md's/do's who are also trained in tcm (traditional chinese medicine & acupuncture). Still, there can be misunderstandings between the 2 areas, as some western doctors don't accept the idea that energy aspects could underlie physiology. Energy is such a basic precept in tcm that fruitful conversation can be difficult.