There are a few things you could do.
You could use transforms with a polyfill like CSSSandpaper to
make it cross browser compatible. Although, to get that type of
separation (with one side of the div being straight) you may have to
use skew AND perspective.
You could make a faux separator by using the before and after
pseudo classes with the CSS triangle trick. This, too, would
require a polyfill for pseudo classes like Selectivizr. You
would also have to play around with the border-width
values to get
it to match what you are looking for.
You could use a PNG using the before/after pseudo classes.
You could use SVG to draw the borders around the containers.
Any of these would work, but its definitely not as easy as, say, rounded corners or drop shadows. You need to put in a little extra work to get those types of results.