And, to extend on that, to what extent is the Chinese civilisation an "uninterrupted" one?
I can't speak to the Yuan dynasty, but the Qing predominantly came from the Manchu region (Manchuria). The Qing emperors adopted many Confucian practices, and because many of the official government and military positions in China were still held by "Han" Chinese, they had to adopt to that culture, language, writing style, etc. In fact, many Manchu emperors (Qing emperors) declared themselves to be Han Chinese.
For your question on an "uninterrupted" civilisation, China went through fits of unification and division, but a sense (or culture, tradition, etc.) of Han Chinese was usually uninterrupted. Again, I can only really speak to Qing China (my specialty), but during the Qing dynasty, China grew at one of its fastest rates, into what is now Yunnan, Tibet, Xinjiang, and Mongolia, why in 1912 Sun Yat Sen's republic had the five major ethnicities - Manchu, Mongolian, Tibetan, Han, and Hui (Chinese Muslims mostly from Yunnan). So even in this period, China is changing alot, and really a broader sense of Han Chinese is exported and constructed into these regions. In the main core of China (the coastal regions) a sense of being Han Chinese (and therefore being a part of Chinese civilisation) develops in contrast to the many other ethnicities that China is coming into contact with. Han Chinese often see Hui, Uighur, Mongol, Manchu as barbaric, uncivilised, etc. and seek to be the opposite (civilised, Confucian, etc.) So I guess you could say that Chinese civilisation is not interrupted during the Qing period, but very volatile. I unfortunately can't speak to other periods, but I hope that gives you a better sense of Qing China.
Sources for Qing dynasty as "Chinese" - its common knowledge that the Qing were from Manchuria. A good source that has a collection of different essays spanning this period is "Dragons, Tigers, and Dogs: Qing Crisis Management and the Boundaries of State Power in Late Imperial China by Robert J. Antony." There are some good articles on ethnicity and on culture. Evelyn S. Rawski also has some interesting (if not controversial) work. "Reenvisioning the Qing: The Significance of the Qing Period in Chinese History" Journal of Asian Studies is good if you can get access to it (don't pay for it). If you want a sense of the progress or continuity of Chinese civilisation that isn't cultural, a scientific or technological understanding of China in best found in Joseph Needham's work. Massive volumes on Chinese science and tech throughout its civilisation. Gives a great sense of the massive scale of Chinese civilisation and its continuity for thousands of years. If you don't have three years to dedicate to his work, a (much) shorter biography is well written by Simon Winchester, entitled, "The Man Who Loved China." Very good work. If you have any more questions on sources I can direct you to some more good stuff.
Askhistorians podcast did something on the yuan dynasty: https://www.reddit.com/r/AskHistorians/comments/2oczhg/the_askhistorians_podcast_episode_25_discussion/
I remember the podcaster stating that the mongols did divorce themselves from a lot of chinese practices. For example they did away with the imperial examination and didn't let han chinese hold high public office. They also repressed the chinese, like banning the carrying of weapons for the han chinese. Hopefully I didn't mis-remember anything.
This is actually somehow an intense, current political issue.
Exactly how Chinese the Qing Dynasty was is up for debate, as shown by many of the excellent posts.
The historical understanding of the Qing was that they were completely (at least largely) sinicized. See: /u/Hahasauce
The consensus among historians in the West has largely turned against this. Mark Elliot is actually very well-known as being a major part of this process. See /u/delaynomoar
This has absolutely outraged Chinese academia and the PRC government, which has begun barring these historians from China.
Of course, the degree of "sinicization" probably varied wildly. The Qianlong Emperor still had a idea of what the "Manchu Way" was, because he could look out to the largely Manchu Northeast. And he could be disappointed by assimilation when he looked at Beijing aristocrats.
The Qing actually spent a lot of time and effort distancing themselves from their Chinese subjects. During the 18th century, the Qianlong Emperor spent a great deal of time and effort bolstering Manchu pride among his banners. He commissioned a book codifying Manchu shamanistic rituals, expelled a great number of Chinese bannermen, and organized great hunts in Manchuria in order to help foster the Manchu martial virtues of riding and mounted archery. In addition, much of Beijing's housing was segregated, with Chinese barred from living in Manchu neighborhoods. The Qing also forced the Chinese to accept many Manchu customs, such as the queue hairstyle, under penalty of death. Chinese historians might argue otherwise, but this is mostly a result (imo) of the inherent nationalism in much of Chinese historiography. It was very important for the Manchus to remain separated from the Chinese, as they were the minority rulers who came into power as a result of conquest. -edit: sentence structure
Mark C. Elliott's book The Manchu Way I feel provide the most comprehensive account of the wide-ranging social and political policies the Manchus have enacted to keep Manchu identity separate from Han Chinese. Some of the points have already been mentioned by /u/GarththeGarth. I don't think I could do it justice by summarizing the book here, digital copies of the book is out there online.
Worth noting, Elliot consulted a lot of Manchu sources that are stored in Japan for his book. Apparently the Japanese were amassing Manchu documents prior to the second Sino-Japanese War with the view of preparing themselves to rule China eventually.