FamilySearch.org has just added a digital collection called "Switerland, Church Records, 1277-1992". This collection is NOT indexed, but it appears to be a complete set of digitized images from the microfilmed church records for the Cantons of Basel-Stadt and Bern.
The images for Basel-Stadt were previously listed as a separate collection, "Switzerland, Basel City, Church Records...", a very misleading title, since the contents cover the entire Canton of Basel-Stadt, and not just the city of Basel. The images within this part of the collection have been reorganized so that it is now MUCH easier to locate the records you need. The corresponding FamilySeach wiki page will need to be updated to help you navigate through the different levels of indexes and original records.