I am not clear what you mean by "appendixing" a response. Do you mean providing a citation that indicates the source of the responses (i.e., the person who provided that quotation)?

I suggest you look at some published articles in your field that used semi-structured interviews and follow the typical procedures provided there.

David L Morgan, I think he means to include the whole transcription of the interviews as an appendix (I guess he is talking about a dissertation).

I mostly agree with the advisor, however, if the interviews were recorded, I would suggest including a dvd or something like that including the recordings (provided permissions are available).

It is always a good rule of thumb to follow the guidelines preferred by supervisors. If you are referring to full transcripts being included in the appendix, the typical approach would be to consider those as the data set of which you will show samples in an appendix if recommended/required by your supervisor, and within the text foe the analysis and findings to show the voice of participants.

You may possibly use any kind of voice to text software (Ex: Speechnote) to convert your interview audio clips.