It depends. IRS allows travel expenses (including airfare) for charitable volunteer work, and Habitat for Humanity is a tax-exempt 501(C)(3) nonprofit organization.
Per IRS guidance, "The deduction qualifies only if there is no significant element of personal pleasure, recreation or vacation in the travel. However, the deduction will qualify even if you enjoy the trip." [https://www.irs.gov/uac/newsroom/tips-for-taxpayers-who-travel-for-charity-work]
Further, from IRS Publication 526: "Even if
you enjoy the trip, you can take a charitable
contribution deduction for your travel expenses
if you are on duty in a genuine and substantial
sense throughout the trip. However, if you have
only nominal duties, or if for significant parts of
the trip you don't have any duties, you can't deduct your travel expenses." [https://www.irs.gov/pub/irs-pdf/p526.pdf, p.5]
Provided your duties and the personal pleasure element align with the above guidance, then your airfare is deductible. Additionally, I find no IRS guidance precluding the level of your airfare (business class vs. coach).
For further reading, here's a link to a TurboTax blog regarding this topic: http://blog.turbotax.intuit.com/tax-deductions-and-credits-2/deducting-travel-expenses-when-doing-ch..., and another to a nicely-written nolo.com article with a section on "travel expenses" [http://www.nolo.com/legal-encyclopedia/can-you-deduct-expenses-volunteering-charity.html].
