This question came up in a train-the-trainer resume workshop I gave last week for resume counselors at a government-funded employment agency. Here's a solution the group came up with:
As one job counselor in my workshop pointed out, it's none of the employer's business that the job seeker was ill, what kind of illness he had, or how he was treated for his illness. He was, in fact, a caregiver during that time -- he was caring for himself (a member of his household).
1. Use years (no months) in the work history.
2. For the gap in employment, list "Caregiver for household member" as the job title.
I thought this was a very creative approach to handling a lengthy illness on a resume. It's honest, doesn't go into unnecessary details, and hopefully keeps the job applicant in the running for a job.