In Reformed theology, are Christians still "totally depraved"?

In 2012, Calvinist pastor [Tullian Tchividjian](https://en.wikipedia.org/wiki/Tullian_Tchividjian) wrote an article, ["Are Christians Totally Depraved?"](http://www.christianpost.com/news/are-christians-totally-depraved-68622/) , in which he applied the language of *total depravity* to both non-Christians and Christians. He argued that the phrase, "as understood and articulated by theologians for centuries, [...] means more than one thing" – both having "no spiritual capacity to incline ourselves Godward" (as non-Christians) and "sin corrupt[ing] us in the 'totality' of our being" (as Christians). Is this the typical understanding of the doctrine of *total depravity* in Reformed theology?