I've done two color ribbing, but I don't remember having any real problems with it.
Knit two with the one color, then put that to the back and bring the other forward to purl two with the next, bring that to the back, knit two, etc. I do all my knitting English, so that may be the difference.
The one thing I don't like is seeing the two color purl bumps when there is a color change in the purl column so I knit the first color change all the way around. You can't even tell.