"Improved Invisibility creates an actual warping of light around the subject that affects technological sensors as well." - SR4A, pg. 209
Between that, and the fact that it would be useless to have it not affect worn / carried objects (and, for comparison, shapechange specifically does not affect worn / carried objects, suggesting that a spell which doesn't will say it doesn't), I favor the shroud approach myself. As such, a dropped item becomes visible, an item picked up becomes invisible when pulled inside the "shroud" of the invisibility.
The question is, where does the shroud begin? Personally, I say it directly conforms to the outer layer of the person, clothing worn, and gear carried. Since the target of the spell is the person, once an item originally cloaked in this manner is removed, it loses the benefits of that cloak. Thus, it would be visible when he picked it up (except where he's holding it), then fully invisible if tucked inside his jacket.
I favor this method in no small part because I like classic tropes such as tossing flour in the air to find the invisible guy, since the field ends at the clothing/skin and doesn't extend out onto new objects. But, if you stick the lemming inside your coat, I'd let it go invisible, too.
All personal preference, of course, since the rules are completely silent on the topic.