You are knitting Combined style. I do as well, and I'm very happy. If you notice, when you do a knit stitch, we do not "twist" our stitches, so they hang over the needle pretty evenly. However, you will notice that the "leading edge" or where you start inserting your needle into the loop is in the back.
So when you do your western purling method, you're not really straightening out the stitch as you do in Continental or western knitting. As a result, we have to do a bit of a different step when we do some increases and decreases. You can find a handy dandy conversion chart here. Also, Annie Modesitt's site is my go to for information when I am knitting combined.
The one thing I have noticed in Combined knitting, and it's always rubbed me the wrong way, is that when you are doing back and forth knitting in stockinette stitch, it can be very ugly if you are not throwing your yarn on the correct way on the purl stitches. Even if you manage to get it to look right, the purl rows appear to be smaller than the rows you knit. It's extremely frustrating. I found that by purling through the back loop (eastern purling) I was able to make my stockinette stitch look even. I do a lot of socks, so the heel flap is really a source of pride for me.
When you are knitting in the round, and I've done a gazillion caps this winter, I didn't have any problem with my ribbing purl stitches and keep doing them in the western fashion, because they are pulled into the background and the knitting stitches pull forward for the ribbing, it all looks fantastic.
You should go to my Ravelry Projects and check out some beanies I've done with a very noticeable K2P2 ribbing. Keep me posted on your project. It's nice to see another active Combination Knitter among us