There are many, many different ways to work knit and purl stitches, and as long as you are happy with the results you're doing it right. While most people knit either English style or continental style, there are also knitters who work what's called combination knitting, so named because it's a sort of hybrid of the two.
I consider Annie Modesitt to be the authority on combination knitting because she's the most famous knitter I know who uses the method, and her book, Confessions of a Knitting Heretic, was where I first learned about the method. She has instructions for combination knitting on her website and also explains her methods in the book.
The purl stitch is somewhat like the continental method of purling except the yarn is wrapped under the needle instead of over it. This changes the orientation of the stitches and requires knitting through the back loop so as not to have twisted stitches.
Modesitt says that knitting combination style makes for a wonderfully smooth fabric with even tension that can be worked up with less strain on the wrists than other knitting methods. She argues that the fact that the knit and purl stitches are mounted differently on the needles makes it easier for knitters to read their knitting as well, and that it makes knitting ribbing faster.
It isn't for all situations, though, and Modesitt says she uses a different method when working Garter Stitch flat or Stockinette in the round (because you're only working knit stitches, your stitches would be twisted if you knit through the back loop without the purl rows).
It also involves some thinking when it comes to shaping garments because of the way the stitches are mounted; you have to think about which way the decrease called for slants and do a decrease that moves the opposite direction to produce the look the designer was going for.