My concern with going to both schools is managing the semesters and the quarters at the same time. I’m sure someone’s done it before and it’s doable, but keeping up with two completely different systems seems like it’s more trouble than it’s worth. Unless you mean taking some quarters at de anza then taking a semester at ohlone or something like that (where you’re not at both schools in the same term), in which case it may be a bit wonky but other than that I don’t see why it’d be a problem.
In addition to what @NCalRent said, utilize assist.org: http://www.assist.org/web-assist/welcome.html. That will let you see what courses transfer to which UCs and CSUs, and what specific requirements they fulfill.