Well color me confused

It's a "thing" for me to always assume I'm missing something when I see someone do something I believe to be wrong. That habit really grew in me when I was still in my conversion process and I was reading Pope John Paul II's Evangelium vitae - his arguments were so contrary to what I'd thought and yet so well thought out I realized I just might not know everything there was to know on a given subject.

So, with that said, I'm assuming that I'm missing something here. Have I missed somewhere that gives permission to proclaim the Gospel at Mass using an alternation of priest, lay reader and song? It went something like this: Father reads a portion of the Gospel, then the cantor pops in for a refrain, then a lay leader reads some, back to the cantor, to the other reader, then the cantor, back to Father and around again. Now I know on Palm (Passion) Sunday it is allowed that the Passion be read in parts, but I have never seen that allowance made for any other day of the year. Did I miss something? I've checked the GIRM, Redemptionis sacramentum and all sorts of sites that Google popped up, but I've not found a single source that suggests this is allowed. Someone tell me I've missed something and that I did not witness the abuse of invention that I think I did. Put another way, there are times when I hate being right, and this would be one of them.