IT’S HARD not to admire Amazon Prime’s “The Marvelous Mrs. Maisel” (TV-MA). It’s also entirely possible to have very mixed feelings about the handsome production from husband-and-wife team Amy Sherman-Palladino and Daniel Palladino, now streaming its second season.

Writing about its first season, I likened it to a musical that never burst into song. Well, this season we’ve got musical numbers. And a period soundtrack featuring Barbra Streisand and cabaret legend Blossom Dearie in the very first episode.

For those who haven’t seen this Emmy-winning series, the utterly charming Rachel Brosnahan stars as Midge Maisel, a wealthy wife and mother of two, seemingly happily ensconced in Manhattan’s Upper West Side in the late 1950s. To everybody’s horror, she leaves her husband, Joel (Michael Zegen), after he has an obvious affair. Chatty and irrepressible, Midge stumbles onto a stand-up comedy stage and spills all of her secrets. This emotional unburdening is seen as a terrifically honest “act,” and she is discovered by aggressive talent scout Susie (Alex Borstein).

“Maisel” follows in the Sherman-Palladino tradition of shows featuring insanely chatty women who get to have their cake and eat it too, while also letting us know how much more cake they want and how they could improve upon the recipe.

On “Gilmore Girls,” Lorelai (Lauren Graham) was presented as both a struggling single mother and a millionaire’s daughter. She lived in a tiny town where everybody brimmed with knowing urbanity. On “Maisel,” Midge is seen as edgy enough to hang out with tortured junkie saint Lenny Bruce and still trot home to Riverside Drive and the life of a cosseted princess. This season she goes to Paris!

Just as “Gilmore” asked us to believe in a character who is city and country at the same time, “Maisel” is both uptown and downtown simultaneously.

I can’t buy it. Real characters are defined by choices and limitations. Like Lorelai, Midge isn’t so much a believable woman as a quip-dispensing device.

At the same time, Midge’s undefined nature makes the more finely drawn characters, like Borstein’s brash and butch Susie and Tony Shalhoub’s absent-minded professor father, all the more enchanting.

It’s hard not to like “Maisel” without hating it a little at the same time. I guess you can have it both ways.

• Discovery launches a live experiment. Every Wednesday for six weeks, it will broadcast “Border Live” (9 p.m.), a look at agents on the U.S.-Mexican border as well as stories of those who live and work in the often-desolate area.

• Ceding the Rio Grande to Discovery, Smithsonian profiles a mighty river on the three-part series “America’s Mississippi” (8 p.m.).

Other highlights

• Duty disrupts a wedding on “Chicago Med” (8 p.m., NBC, TV-14).

• A financial deadline looms on “Empire” (8 p.m., Fox, TV-14).

• Floki ponders the will of the gods on “Vikings” (9 p.m., History, TV-14).

• “Mysteries at the Museum” (9 p.m., Travel, TV-PG) recalls the CIA’s attempts to heist a Soviet satellite.

• The former first lady discusses her recent memoirs on “A Thousand Words With Michelle Obama” (9 p.m., BET).

• The river of addiction flows on “Chicago P.D.” (10 p.m., NBC, TV-14).

• A change of scenery on “A Million Little Things” (10 p.m., ABC, TV-14).

Cult choice

Marcello Mastroianni and Sophia Loren star in the 1964 Italian melodrama “Marriage Italian Style” (8 p.m., TCM), directed by Vittorio De Sica.

Series notes

Visits from home on “Survivor” (8 p.m., CBS, TV-PG) ... Bachelor party blues on “The Goldbergs” (8 p.m., ABC, TV-PG) ... Archie becomes a fugitive on “Riverdale” (8 p.m., CW, TV-14) ... Katie recalls her frisky youth on “American Housewife” (8:30 p.m., ABC, TV-14).

Fears of a mole grow on “SEAL Team” (9 p.m., CBS, TV-14) ... Red asphalt on “Chicago Fire” (9 p.m., NBC, TV-14) ... Legal woes on “Star” (9 p.m., Fox, TV-14) ... Ed Begley Jr. guest-stars on “Modern Family” (9 p.m., ABC, TV-PG) ... Spencer makes his choice on “All American” (9 p.m., CW, TV-14) ... Will has an agenda on “Single Parents” (9:30 p.m., ABC, TV-PG) ... A suspicious rise in overdose deaths on “Criminal Minds” (10 p.m., CBS, TV-14).

Late night

Expect Jeremy Scott on “The Daily Show With Trevor Noah” (11 p.m., Comedy Central) ... Jeff Daniels and Emily Mortimer are booked on “The Late Show With Stephen Colbert” (11:35 p.m., CBS) ... Jimmy Fallon welcomes Anderson Cooper, Andy Cohen and John Legend on “The Tonight Show” (11:35 p.m., NBC) ... Jennifer Aniston, Chris Elliott and Rita Ora appear on “Jimmy Kimmel Live” (11:35 p.m., ABC, r).

Howie Mandel, Danielle Macdonald, Mehdi Hasan and Nikki Glaspie visit “Late Night With Seth Meyers” (12:35 a.m., NBC) ... Jude Law, Steve Coogan and Sam Morril appear on “The Late Late Show With James Corden” (12:35 a.m., CBS).