There are several things you can do to demonstrate that you recognise and/or appreciate the importance of Chinese history and culture. A few of them are explained below.
Learn some basic Chinese
This is one of the simplest ways to actively show your appreciation of Chinese culture. The effort to communicate in your partner’s language, no matter how hesitantly, is a courtesy that will be well regarded.
Refer to Chinese historical sites you may have visited with enthusiasm
Even if you were disappointed by the actual grandeur or condition of these sites, they are considered important representations of China’s long history.
Avoid making depreciating comments, even in jest
This applies to any aspect of Chinese culture or history. What you might intend as a light-hearted observation will not necessarily be shrugged off by your host as an uncouth comment made by an ignorant foreigner.
They may feel obligated to defend whatever aspect of China you have depreciated, whether out of genuine pride or a habit acquired during the Maoist era when all Chinese were constantly drilled in the notion that China was a great country that would surpass the world’s other great nations one day.