Assuming you're single, taking the lump sum would put about $30K of your income (that year) in the 33% tax bracket. The rest would be unaffected. If you took the annual payments, all of your pay would remain int he 28% tax bracket. So you would end up losing around $1,500 upfront due to increased taxes.
However, if you plan on putting that extra upfront money towards a down payment, there would be a huge saving even with that 5% lost, to the tune of around $3,000-$4,000 per year (assuming you put all $100K towards a downpayment and your interest rate is around 3-4%.)
So yes, you would end up paying a little more in taxes, but you would end up owing a LOT less in interest over 10 years.
One thing to keep in mind: I don't know how the aviator bonus works but I assume you owe 10 years (given that it's paid out over 10 years) afterwards. If it works like other retention/affiliation bonuses (I only know Army), you have to pay it back prorated if you can't complete that committment for any reason other than something totally outside your control. The risk of putting all $112K towards a mortgage (rather than say, a mutual fund or something a bit more liquid) is that you're up a creek if for some reason you have to pay a portion of it back.