I love two-color ribbing (also called corrugated ribbing) and I think it can really enhance a knitting project. The knitted stitches are one color and the purled stitches are another color. Because of all the floats it is slightly less elastic than regular ribbing.
If you are a two-handed color knitter, doing this type of ribbing really isn't much slower. I am right-handed and I hold the yarn that is to be purled in my right hand and purl those stitches American/English style and the yarn that is to be knitted in my left hand and knit continental.
I'm not sure why so many knitting patterns change colors in two-color ribbing in the purl stitches. That requires that you knit across the first row every time you change a color (to avoid bi-color purl bumps) and it can really affect the elasticity of the ribbing. I always change colors in the knit stitches instead.
One oddity about two-color ribbing is that if you cast on in one color using the long-tail cast on and then immediately start the ribbing the color you didn't cast on with will tend to peak out under the cast on edge. I don't think the problem even has to do with your tension on the first row - the problem seems to be that two-color ribbing makes the bottom edge curl up slightly. It isn't a huge problem but it annoys me. I pulled on the pink yarn a bit to further demonstrate this problem at the bottom of the knitting in this checkerboard two-color ribbing.
I've heard there may be a special cast on you can use to avoid this but I'm not aware what it is. I've even had this happen even when I cast on with two colors. Let me know if you know of a cast on that eliminates this. One easy way to avoid it is to rib the first row in the cast on color and start the two color ribbing on the second row.
I am not always fond of how this looks though so I use another solution.
If it is really bugging me I go back after I'm done knitting the item with the cast on yarn threaded in a tapestry needle and LOOSELY tack up the bottom float. Here you'll see the diagonal white yarns on the bottom of the Checkerboard Mesa hat from yesterday's post that have been tacked up.
Here is another photo that shows what the interior of corrugated ribbing looks like.