While these sciences are not history research themselves, all three use eachothers tools and knowledge interconnectedly. Hell, my favourite stuff to learn about is microhistory, which is a pretty solid mix of these.
However, I have had multiple seminars and classes about the topic, and could never figure out the difference that makes anthropology and ethnography separate sciences.
At the end of every article of literatue on the topic, the only difference I can see is that Ehtnography is the kind of Anthropology that needs no passport to research.
You may also want to submit this question to /r/Askanthropology. In the US, anthropology departments frequently include the fields of archaeology, ethnography, demography, linguistics, and primatology. By that definition, ethnography resides under the umbrella of anthropology. Ethnography is generally taken to mean the study of culture and one of the fundamentals in the early way it was practiced was that one should remove oneself from one's own culture - and study another culture to gain a better perspective. In Europe, this created the situation where ethnography was often the study of colonial cultures, and the discipline of folklore stepped up for the study of European cultures, often using similar methods, but just as often resulting in distinct bibliographies. In Europe, archaeology and ethnography are frequently in separate departments, again because the former often began with the digging up of European antiquities while ethnography/anthropology was more of the study of colonial cultures.
In the US, archaeology and ethnography frequently found common ground because they were two expressions of the study of Native Americans and other cultures. They had overlap in same methodology and goal - namely to understand the culture of other people (one removed geographically and/or culturally and the other removed by time).
edit: adding linguistics - how could I forget that?!?