Resume: put down facility or agency??

So a lot of people are telling me a whole bunch of mixed information. I work at a nursing home that largely hires agency nurses (me being one of them). I have a full-time schedule, and I'm a regular on my floor for my shift. I'm creating my resume and I put down my agency under work experience but others argue that I should put the nursing home. I don't want an employer to think I'm deceiving them, but I don't want them to look at my resume and be taken away because I'm an agency nurse; especially since I'm getting the same experience as if I was a full-time direct hire. I know I can explain my situation in a cover letter, but where is my work performance reference coming from?
I would put down both. Put the LTC down as a sub category under the agency.. Just my opinion.

I have done what realnurse says, listing it something like this: Horatio Hoover Nursing Agency, Bella, Togo with duty at Lola Longacres Old Folks Emporium.

I put the agency as employer, then under that-list all the facilities I worked at. If you worked at one place full time, list the dates you were there. This shows you can integrate well. If they kept you they must like you. Good luck!