Hi Justin， "给我看一下您的护照" much better. 因为这个句子的基础句型是给某人看某物。给Somebody 看something. “一下”和“您的”是做补语和定语。 在海关等正式场合，其实更喜欢说：请您出示下您的护照。 （出示：show， please show and let me see) 希望对您有所帮助~谢谢~

It is supposed to be "请给我看一下您的护照“ Here 请=please, it's very important to add this word or it may sound aggressive and rude. By the way, the real situational dialogue, we say “ 您好，请出示您的护照。” Here, 出示=show， which sounds more polite since it's a formal expression. 给我......= give ......to me, which sounds like an order.

They both sound right. The latter sounds slightly less formal so you are probably more likely to see the first from a textbook. Usually sentences ending with 一下 sounds a bit informal(not without exceptions like 请等一下, which is quite formal). You can also say 您的护照给我看一下 which also sounds slightly informal。 Hope this helps.