Most airlines will tell you that the first segment should be treated as international in terms of airport arrival and check-in. This is because with most airlines, the initial "document check" is performed at that point, since you generally will be issued boarding passes for the int'l segment at that point and won't check in at all at the connecting city. But, this is mostly just a precaution, for example in case there's a question about your documents that requires them to check with someone else. If you are traveling in a "normal" situation, such as a US passport going to a country that doesn't require a visa in advance, the "document check" should take all of 10 seconds.