The promotion runs from December 1 to February 28,2013. You need to use code SWADBL when making the booking and choose Jet, Etihad or Qatar as your partner airline.
I have not been able to find other airline related Hyatt promos for this time period, but they may be around.
Hyatt Capital Gate, Abu Dhabi, Park Hyatt Abu Dhabi Resort & Villas, Hyatt Regency Chennai, Park Hyatt Chennai, Hyatt Regency Delhi, Grand Hyatt Doha, Grand Hyatt Dubai, Hyatt Regency Dubai, Park Hyatt Dubai, Grand Hyatt Goa, Park Hyatt Goa, Park Hyatt Hyderabad, Park Hyatt Jeddah Marina, Club and Spa, Hyatt Regency Kathmandu, Hyatt Regency Kolkata, Park Hyatt Maldives, Hyatt Regency Mumbai, Grand Hyatt Mumbai, Grand Hyatt Muscat and Hyatt Regency Pune.
Double miles offer valid December 1, 2012-February 28, 2013 with Etihad Airways, Jet Airways and Qatar Airways at participating Hyatt hotels worldwide. All hotel reservations are subject to availability and must be made in advance. Offer is not valid with groups/conventions and may not be combined with other promotional offers. Guest must request offer code SWADBL at time of reservation and check-in to receive bonus miles. Guest must choose miles for their stay. Guest must present a valid airline membership card at check-in and pay an eligible rate. An “Eligible Rate” is any hotel published room rate, including, but not limited to rates found on hyatt.com or any Hyatt Gold Passport, the Hyatt Daily Rate, Volume Rate, AAA and Senior Citizen rates, etc. “Ineligible Rates” are discounted rates, including, but not limited to, any free night stays, Internet wholesale rates (such as priceline.com, hotels.com, etc.), traditional wholesale rates (such as GOGO Worldwide Vacations, Pleasant Holidays, etc.), airline crew rates, airline employee rates, travel agency employee rates, Club at the Hyatt discount certificate stays, Hyatt Vacation Club stays, Hyatt employee or employee family discount rates, airline interrupted-trip vouchers or contracted rooms (a contract room is a room that has been reserved pursuant to a written and executed agreement between a hotel and a corporation, government agency or individual for a negotiated room rate in exchange for an agreed upon number of rooms to be rented for an extended period of time). One bonus per member, per room, per stay. Eligibility for miles is subject to the terms and conditions of participating airlines programme. Allow 6-8 weeks after your stay for your bonus miles to be posted to your airline account. This promotion is subject to the Terms and Conditions of the Hyatt Gold Passport program. One bonus per member, per room, per stay. Offer is subject to terms and conditions of the Etihad Guest Miles program.