Interview, taking, giving, being interviewed

Solution 1:

The third option is preferable for both cases.

For the first case, the interviewee may 'take' an interview if an interview is offered to her:

I am taking the interview offered by Company X, but not the one offered by Company Y.

The interviewee may also 'give' an interview if it is asked from her:

I am giving an interview to Journalist X, but not Journalist Y.

These uses are customary: companies customarily offer interviews to candidates; journalists customarily ask for interviews from prospects.

For the second case, the interviewer may give an interview to a candidate or prospect who has requested one or who has been offered one. It is unusual phrasing for an interviewer to take an interview, but it does occur; when it does occur, the phrasing (in my experience) is usually jargon, that is, specialized language used by a human resources or another professional who interviews professionally.

However, if a journalist, human resources professional or another interviewer is offered an interview by someone from whom an interview has not been requested, the interviewer might without using jargon say that they are taking the offered interview.

During an interview, if an interviewer asks the interviewee directly something obnoxious along the lines of "Are you giving [me|us] this interview, or are you taking it from [me|us]?", the appropriate response is determined by the circumstances. In the bare circumstance described, my inclination would be to fall back on the third option: "I am interviewing with you because [something]", supposing I want to continue the interview in that circumstance.

If an interviewee asks an interviewer the same question, the response will also be suggested by the circumstances. The interviewer might fall back on the third option (just as the interviewee did in like circumstances), "I am interviewing you because [something]", supposing the interviewer wants to continue the interview in that circumstance.