If you are using an even-number of stitches in the i-cord, then you can cast-on with knit-purl pairs when working Italian cast-on. For odd-numbers of stitches in the i-cord, you'll need to start with a purl rather than a knit. Notice, too, you can use a cable needle to rotate stitches to make them more knit-like or purl-like, as you need.
When transitioning to a tubular bind-off, work the same maneuvers you did to transition into the i-cord, but work those steps in reverse. A tubular bind-off to match Italian cast-on takes two "rows":
Row 1: alternate knit 1, slip 1 purlwise with yarn in front. The knits will all be knit, and the purls will all be slipped. Can be started on the knit or slip, depending on whether you have k1, p1 or p1, k1 on the needle.
"Row 2": Kitchener graft knits and purls together as if they were a sock toe. Dividing the knits and purls on to separate needles is helpful for many people, since that set up resembles a sock toe ready to be grafted closed.