Preemptive disclaimer: I am one mathematician, and this is only my experience. That experience is based on applying to tenure track positions at major American research universities, and being male.
My wife works as a clinical research assistant, meaning that she runs experiments, files paperwork, recruits subjects and applies for grants, but she is not an academic and does not do her own research. She currently works at a hospital with a major research program; she has worked in university labs in the past.
My pattern, based on the advice of several older mathematicians, was to omit my wife from the paper applications but mention her early in the interview process. At times I brought this up when the chair first called me; more often I brought it up at the beginning of our face to face interview. My thinking was that I would not go anywhere that my wife could not find work, so it would be best to bring this issue up head on and find out how the university would respond.
Everywhere I did this, I received a very positive and supportive response. Chairs and deans promoted the opportunities for my wife in their campuses and cities, and offered help in finding work. I did not try to get a commitment that my wife would be hired by the university, because my understanding is that it is not reasonable to ask for that sort of commitment for a nonacademic position, but I did attempt to determine whether it was likely she could find work at or near the university.