Double Knitting Bind Off question

I’m quite confused about this. How do I make it so the front color stays in front and the back color stays in the back while binding off? Or is that impossible?

I suspect it’s largely impossible but you never know what people might suggest. I just cast off in two yarns but they were harmony colours and it didn’t matter. I guess you could see what you happen - via swatching - if you passed over one strand first and then the other. Whether the second would affectively sit on top of the other.

Oh, I had also intended to mention that it may not be one in front of the other but one of top of the other. At least that’s my bindoff in K generally looks. It’s at a sliggghhht angle but not much.

So do I bind off every stitch then? Knit, pass yarn over to bind off, purl, pass yarn over to bind off? Thanks for you help!