Audio guy here. There are two general types of stereo audio files that can be created from a music production/editing system: interleaved, and, non-interleaved. These terms refer exclusively to stereo audio files.
In an interleaved file, you have a single file containing both L and R sides of a stereo recording. A non-interleaved file is always two files, one for L, the other for R. It's almost always referred to as a non-interleaved
file even though there are two separate files for that piece of audio.
As you probably know, there are many pro audio DAW software packages available. Of them, ProTools natively handles the L and R sides of stereo audio as separate files, often referred to as "dot L" and "dot R". For example, if you imported an interleaved file into ProTools, it will automatically convert the file into separate .L and .R files. So to your question specifically, if you were to export interleaved files, and your client is working on ProTools, they will (not "should" but "will") not encounter any difficulty in handling your interleaved file. PT will take care of the conversion.
Having said that, some PT operators moan about getting interleave files. Frankly I don't get it, as they don't have to do anything but wait a few seconds for PT to create a non-interleaved version. But I thought I'd throw that in FYI.
Other audio DAWs give you a choice of file format: sd2 (sound designer 2, the PT native format, which is usually non-interleaved, though some DAWs let you create interleaved sd2 files), and then there are the cross-platform compatibile wav and aiff file types (which are usually interleaved).
Apple's Logic Pro gives you the choice to work in, or export, almost any file format, including interleaved and non-interleaved versions of aiff and wave amongst others.
Now, to MONO files. In the audio realm, mono audio files are never referred to as "interleaved" or "non-interleaved". Mono is just mono. Sometimes, however, mono audio will be recorded onto a stereo track, meaning that both L and R sides contain exactly the same thing. This is sometimes done for a variety of reasons that I won't get into. In this case you your file -- regardless of format -- is a stereo track. And audio people always make it a point to hip the recipient of such a file that the file is a mono "track" in stereo format.
Maybe I went a little too far with this explanation, but I was on a roll! HTH.