Brad Woodhouse, left, and Sean Spicer goof around outside Bullfeathers, site of their joint fundraiser for military public affairs officers. (Marvin Joseph/The Washington Post)

Even when Sean Spicer and Brad Woodhouse got booked for a little feel-good segment on MSNBC on Monday morning, it was hard for them to stop debating.

Spicer, the Republican National Committee spokesman, was gloating over dire poll data for President Obama: “There isn’t a battleground state where he’s doing well.” Woodhouse, his counterpart at the Democratic National Committee, parried with other stats: “Quinnipiac came out, and we were beating every Republican by five points or up to double digits.”

Would you guess these guys are friends? Somehow they are — not just despite their roles as opposing mouthpieces in a partisan town, but also because of it.

On Wednesday night, the peculiar partnership of Woodhouse and Spicer was on display at a party they co-hosted at Bullfeathers on Capitol Hill. “Flacks for Flacks Who Wear Flak Jackets” — a bursting-at-the-seams fundraiser to provide holiday care packages for military public affairs officers in Afghanistan. (And yes, they got around to flacking it that morning on MSNBC after they stopped bickering.)

The two speak at least once a week to coordinate on matters such as the primary calendars or their bosses’ Sunday talk-show appearances. About once a month, they go head-to-head on cable news. But they always part ways collegially.

Team of rivals: Woodhouse and Spicer (Marvin Joseph/The Washington Post)

“There’s not a thing that I agree with Sean on, policy-wise,” said Woodhouse, 44. “But on a personal level I certainly like Sean a lot.” (The Democrat knows a bit about bipartisan relationships: His wife is a Republican, chief of staff for a Tea Party freshman.)

When Spicer, a Navy reservist, suggested the Flacks benefit, Woodhouse signed on right away. “From a personal standpoint, the sacrifices these guys are making during the holidays are just unreal,” Spicer told us. More than 100 political reporters (including a couple of our colleagues) and operatives from both sides of the aisle added their names to the host committee.

Alas, the GOP debate meant the magic night of unity would end at 8 p.m. on the dot, as both men headed back to their offices. “[Sean] will send out missives and tweets and all that attacking the president,” Woodhouse told us, “And I’ll be sitting here at my desk sending out tweets and missives attacking the Republican candidates. This bipartisanship can only go so far.”