Well, let's go look at the FAR, shall we? 61.51(f):
(f) Logging second-in-command flight time. A person may log second-in-command time only for that flight time during which that person:
(1) Is qualified in accordance with the second-in-command requirements of § 61.55 of this part, and occupies a crewmember station in an aircraft that requires more than one pilot by the aircraft's type certificate; or
(2) Holds the appropriate category, class, and instrument rating (if an instrument rating is required for the flight) for the aircraft being flown, and more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is being conducted.
So, if the airplane requires two pilots on it's TC, and you're qualified in accordance with 61.55, you can log the time and SIC. I think (but can't quote a reg) you can log the X/C time too.
If the airplane DOESN'T require two pilots, but the 91K regs or the OPSpecs do, then you can also log SIC time.
A type rating isn't required for SIC time, as I read the regs, if the flight is domestic in the US.