The “Madam Secretary” cast and crew surround former Secretary of State Madeleine Albright. Photo by Emily Heil.

The ongoing love affair between Real Washington and Onscreen Washington got steamier on Thursday night at the screening of the new CBS drama “Madam Secretary” at the Institute of Peace.

So there was former Secretary of State Madeleine Albright getting a round of applause upon her arrival on the red carpet from the cast, including Tea Leoni, the actress who plays an unconventional SecState, a former CIA analyst plucked from academia; Tim Daly, who plays her Georgetown-professor husband; Bebe Neuwirth, who portrays a steely chief-of-staff; and Morgan Freeman, the show’s executive director.

And there was Freeman, chatting up Maureen Dowd; CBS newsman Bob Schieffer (who has a cameo in the show’s premiere episode) mingling with the actors who play young Foggy Bottom aides; and Daly, shooting the breeze with Philippe Reins, the longtime aide to another former SecState, Hillary Clinton.

So let’s get one thing straight: Elizabeth McCord,  Leoni’s character, IS NOT HILLARY, PEOPLE. “Kissinger!” the actress responded when asked which real-life diplomat-in-chief she emulated, gesturing to her slouchy pantsuit.

And Daly tried to preempt the critics who might perceive the show as a pro-Clinton docu-drama, given its “West Wing”-like reverence for governance that’s so unlike many other installments of the Fake Washington genre (see the dark and treacherous side in “House of Cards,” or the delightfully neurotic folks of “Veep”).

“It’s not some liberal Hollywood conspiracy to elect Hillary,” he assured us.

Meanwhile, Real Washington was enjoying the moment. Albright was all smiles, and Reines tells us that the show gets plenty of details right.

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