The context doesn't make things much better, nor the fact that it came from Augustine, the darling of some reformers, including this:
"About Jesus Christ and the Church, I simply know they're just one thing, and we shouldn't complicate the matter."
I think it is more complicated than that. Is Jesus really only half a person without the Church???
Rom 12:5 so we, though many, are one body in Christ, and individually members one of another.
I Cor 12:27 Now you are the body of Christ and individually members of it.
Col 1:24 Now I rejoice in my sufferings for your sake, and in my flesh I complete what is lacking in Christ's afflictions for the sake of his body, that is, the church,
Scripture is pretty clear about it.