Clearly employers should not be asking references about candidates' personal situations and how these will affect their willingness to take a job. But most certainly this does occur, so prepare your references. Rather, proceed with your search as if you are a single entity so that you can be judged on your own candidacy. However, if you're applying for the same job and your vitas make it obvious that you're a couple, for instance by having the same last names, addresses, and phone numbers, you should probably discuss the issue in the letter. Either let the committee know that neither of you wants the other's candidacy to interfere with full consideration or, if it interests you and you can afford it, raise the issue of job sharing.
Job sharing, however, is usually a long shot.
In the more common case, where only one of you is applying to a department, the hiring committee's need to know about your status depends entirely on whether you will only take the job if your partner finds one in the same city. If you are both willing to commute, avoid bringing a partner's situation into the discussion until after receiving a job offer. If the topic comes up earlier, stress that you will commute and you each are looking for the best individual fit. If you truly won't take the job unless your partner gets one in the same city, you should probably make this known before accepting a campus visit and definitely before getting to the point of a job offer. Otherwise you risk having the hiring department feel you've concealed important and relevant information from them, hardly a good beginning in a new position.