Trini,
If you don't have an FAA license, then you can't log the time at all, regardless of who you fly with, unless the other person is an instructor. If you don't have time to get the paperwork done for your "based on a foreign license" license, then you can either get an FAA Student license (if you don't want to carry pax), or an FAA PPL (if you do). Not exactly sure what's involved in the latter, but the former should just be a case of getting signed off by an instructor (and probably an FAA medical, too, but I'm not sure).
If you're flying with someone else, on a valid license (as above), then, in general, only one of you can log the time. There is one exception to this: that is, if one of you is P1, under foggles, then the second person is Safety Pilot. Safety Pilot time does not count towards any JAR license or rating, and can't be logged under JAR rules, but it can be logged under FARs. So, whichever of you is not under foggles, you can count that time towards any minima that the FAA specify for future FAA licenses and ratings.
Hope that answers the question... it starts to get quite complicated.
FFF
-----------