The Interlaced Band stitch is what's called a combination stitch. You start with a basic foundation stitch—in this case two rows of back stitch—then you work another thread on top. I found this in a vintage embroidery booklet and I'm going to include the drawing that illustrated it along with the usual photos. It seems a bit tricky at first but once you get the motion down it will get easier.
Start by working two parallel rows of back stitch about 1/2 inch apart. They should be exactly even in length (one reason I used a fabric with a very visible weave) and the second row should have the end of one stitch directly in line with the center of the stitch above it.
Thread your needle with a second color and come up between the rows and in line with the left side. Now go over and under the first stitch in the top row.
Pull the thread through so it forms a loop but don't pull too tightly—you want to stay centered on that first stitch and not pull it down.
Now, take your thread over and around the first stitch in the bottom row.
Continue this motion, alternating between the top and bottom rows of stitches, always going over and around and keeping your needle on top of the thread in the center.
Here's what it looks like when you've finished.