You have several options:
1) The most robust solution is to explicitly state the copyright license in every file. It can be a single line at the top:
// Copyright (c) 2016 Your Name. Licensed under the MIT license (see LICENSE.txt).
This removes any doubt about the licensing and copyright of any given file.
For the third-party software, do the same (but pointing to separate LICENSE-FOO.txt file), or just include the entire license text in a comment blurb at the top.
2) Alternatively, you can add this line to the top of your LICENSE.txt:
Except where otherwise stated, this code is:
and then add a blurb stating otherwise to the third-party software files (as in option 1).
3) Finally, due to the wording of the MIT license, you can actually merge the licenses of multiple MIT licensed works into a single MIT license with multiple Copyright statements:
Copyright (c) 2016 Foo
Copyright (c) 2016 Bar
Permission is hereby granted, etc.
Just make sure to preserve the original Copyright statement(s) verbatim, and make sure that the rest of the two MIT licenses texts are actually identical word-for-word (unfortunately, people sometimes "tweak" the text, meaning the "MIT license" is not longer actually the real MIT license).
While legal, this can be confusing, since it's not clear which files originated from which author.