Is there a term that describes choir and congregation singing verses or chunks of a piece alternately? I'm thinking for example, of Credo iii which (at the Birmingham Oratory at least) is sung in alternating manner between choir and congregation, swapping at the double bar lines.
I understand that decani and cantoris is a term indicating the Dean's side and the Cantor's side alternating. Maybe there ain't one. This is the place to find out though.
Another possible term would be alternatim. This would be good, echoing the French practice of singing v. organ versets, and thus closer to congregation v. choir.
Antiphonal has come to mean "side-to-side", as in Dec and Can, as Gwyn states. However, Gelineau in Voices and Instruments in Christian Worship used "antiphonal" to mean "with an antiphon" [i.e. at the beginning and end], and preferred the term "alternating [psalmody]" to speak about side-to-side singing.
To complicate matters, though, alternatim tends to be used where the two groups have different arrangements of the music, e.g. Henry Washington's marvellous alternatim adaptation of Monteverdi's Ave maris stella, from the Vespers of 1610, which alternates plainsong with choral music.