Per Schengen visa requirements (article 15) any traveler must have a medical insurance with 30000 EUR coverage. The permanent resident in the US has BlueShield/Bluecross coverage with the BlueCard Worldwide® Program. A letter is needed stating that the said person has coverage and appropriate benefits.
A call to Bluecard resulted in nothing. They do not know what is this all about as majority of their customers are US citizens, not permanent residents.
Additionally, I found information about a Canadian person that was able to request a letter from HR and about a possiblity to get the similar letter from the credit card you used to buy your ticket.
How to obtain one? Does this coverage verification letter has some name one can refer to? Whom do I need to contact?