Part three of the Double Knitting series is all about how you work your color changes.
Remember, I use the terms blue and white yarn here because I think it’s easier to understand which thread is meant than saying main color and contrast color.
Double knitting creates a two-layer fabric. The stitches are worked in pairs. If you are aiming for stockinette on both sides, one pair consists of one knit and one purl stitch. In order to keep the yarn not worked for the stitch in between the two layers so there become invisible, it has to be behind the worked stitch when knitting and in front of the worked stitch when purling.
If you don’t like handling two threads at a time you can slip the stitches of one color for one row/round, switch to the other color and work the stitches with this color. This takes much longer, because you work every round/row twice.