faculty application - How reasonable is it to ask my referees to send their recommendation letters to me?

I am applying for a junior faculty position (i.e. tenure track assistant professor level) at a research-intensive US university this fall. As a part of the application process, the university asked for CV, cover letter, employment application letter, a list of referees at the initial phase. Now they have contacted me again and asked to submit three reference letters, a teaching statement, and a research plan via email in order to complete my application. Most interestingly for the reference letters, I have been given the options of having my references email them directly or I can forward them their letters. I can do whichever is more convenient to me. My concern is with the second option. If I ask my referees to send their letters to me, I can see what they are writing about me. Will they feel secured in such a way? Please advise how I should proceed in this regard.