I applied online. The process took 4 months. I interviewed at Solidarity Bridge (Evanston, IL) in Apr 2014
Interview
The whole process took 4 months. Three interviews spaced out, as staff was travelling and/or on vacation. While they are a Catholic organization, they specifically state in their materials that they do not proselytize, nor discriminate according to religion, sexual preference, etc. All in all, they promote themselves as a progressive organization promoting social justice by way of medical missions to Bolivia and Paraguay.
Before the first interview I was asked to write brief essay answers to several questions. I interviewed with three people in English and Spanish. The second interview was with 6 people, including board members. At both interviews, the topic of religion was almost an aside. In fact the only mention of religion in the written job description was the very last bullet point "able to articulate the religious basis of the mission work"
The last interview was again with three people. They told me that they were very impressed with my non profit background, especially in international development, but they wondered why I didn't talk about God as my motivation. Then the kicker: "Are you a disciple of Christ?" Trust me when I tell you that after 4 months of preparation and interviews I very nearly had a very unchristian answer for them.
One year later, their job search is still open.