The technique you are using sounds like "combined knitting" aka "eastern uncrossed knitting" (Amy has videos on "combined knitting"). It's a style that is apparently the norm in Eastern Europe, the Middle East, and central Asia.
When you knit this way, your stitches end up mounted the way you described.
Re knitting in the round using this style of knitting: the other day I came across a website which has a video about eastern uncrossed knitting in the round:
You have to scroll to the bottom of that webpage, and click on the link to "Eastern Uncrossed Knitting - one video
learn "in the round" technique for Eastern Uncrossed Knitting
same page as Socks on Two Circulars".
Unfortunately I haven't been able to watch the video because my computer freezes up everytime I try to download the quicktime plugin, so all I have been able to do is read the information there.
I hope the link works for you! If not, I know there are other combined knitters on this board who may be able to give you advice.