I recently ran into Knit 1, Purl 1, Knit 1 in the same stitch on a free pattern on Yarnspirations. It was called the Knit Texture Blanket. One of the squares inside of the blanket has this stitch pattern.
The stitch essentially increases 1 stitch into 3. I was confused on how to do all of this in one stitch. So I turned to my knitting mentor on how all of this is possible inside one stitch.
This particular stitch appears with a stitch called Trinity Stitch. It's a repeating of this stitch combo followed by Purl 3 Together (p3tog). In the tutorial below, I show you how to do only the Knit 1, Purl 1, Knit 1 inside the same stitch.
For more information and written instructions: http://theknitcrowd.com/lets-knit-knit-1-purl-1-knit-1-in-same-stitch