22nd July 2015 From India, Chennai
There's no harm showing your H1-B to your Company....PROVIDED there's clear understanding that you will be relieved based on that Doc.
Your HR may be asking for it to confirm for themselves that you aren't bluffing....since H1-Bs aren't that common now-a-days as they used to be few years back.
And DON'T give your Passport even for a sec--just give them a xerox copy of the H1-B Visa Stamped page.
All the Best.
23rd July 2015 From India, Hyderabad