interchurch, interdenominational

from The Collaborative International Dictionary of English v.0.48

nonsectarian \nonsectarian\ adj.
   not restricted to one sect or school or party; as, religious
   training in a nonsectarian atmosphere; public funding is
   restricted to nonsectarian colleges. Opposite of {sectarian}.
   [Narrower terms: {ecumenic, oecumenic, ecumenical,
   oecumenical}; {interchurch, interdenominational};