From the IRS' website:
How many annual exclusions are available?
The annual exclusion applies to gifts to each donee. In other words,
if you give each of your children $11,000 in 2002-2005, $12,000 in
2006-2008, $13,000 in 2009-2012 and $14,000 on or after January 1,
2013, the annual exclusion applies to each gift. The annual exclusion
for 2014, 2015, and 2016 is $14,000.
What if my spouse and I want to give away property that we own together?
You are each entitled to the annual exclusion amount on the gift.
Together, you can give $22,000 to each donee (2002-2005) or $24,000
(2006-2008), $26,000 (2009-2012) and $28,000 on or after January 1,
2013 (including 2014, 2015, and 2016).
Basically, this means that it doesn't matter which person it specifically comes from as it's a "joint" gift.
There is more complicated paperwork to fill out if the gift comes from a single check and needs to be "split" for taxes. Each parent would need to fill out a separate gift tax return form, essentially proving that both parents approve of the gift. It seems like it's easier if each parent writes a separate check, however it's not a requirement.