Actually, I think the interviewing companies are looking for proof of your US citizenship. An official passport is one easy way to confirm this. Whether the red diplo passport would satisfy this requirement is questionable. We have several pilots flying at UPS that are non-res aliens, or res-aliens -- both carrying their green card and resident countries passport.

Once you get onboard an airline who's schedules requires passports and visas, how you get them and who pays is up to each company or your contract.

At UPS, all fees for passport and visa applications, and renewals are paid for by the company. They even expidite it, so you get it back within ten business days. For new hires, this is done during BI, depending upon your fleet/domicile assignment.

One pain is that the passport is usually good for ten years, but many visas (like the PRC) are only good for two or five years, so you've gotta stay on top of them.