As splashy thrillers of every style and subgenre proliferate on platforms clamoring for viewers’ rapt attention, what increasingly separates the ones worth getting hooked on from the ones that are just wasting our time is a single quality: tone. They all feature a marquee star or two. Many, from Alfonso Cuarón’s Disclaimer to the ever-expanding David E. Kelley canon, also boast a prestigious or at least famous creator. Most are adapted from bestselling suspense novels. And they invariably move at a whiplash pace, leaving big blanks to fill in and a cliffhanger at the end of each episode. But none of these enticements can conceal the absence of scripts and direction that set a distinctive mood, then deftly navigate every deliberate shift. With belt-cinching streamers straining to do more with less, sloppy vibe calibration has become a common problem.

Such is, unfortunately, the case with His & Hers, a Netflix crime thriller that promisingly casts Tessa Thompson and Jon Bernthal as estranged spouses who suspect each other of murdering a woman they both knew. Created by William Oldroyd, a filmmaker who made his name with the acclaimed big-screen psychological thrillers Lady Macbeth and Eileen, it comes with a cinematic pedigree. It relocates a popular novel by British author Alice Feeney from the UK to Hollywood’s cost-effective new production mecca, Georgia. There’s an echo of Mr. & Mrs. Smith (the Brad Pitt-Angelina Jolie spy movie more than Donald Glover’s series-length riff on it) in both His & Hers’ title and its premise; sex, violence, ambition, and mutual mistrust propel the six-episode arc. The trouble is that Oldroyd never quite decides how seriously to take the story he’s telling. Arch at some moments and grim at others, the show ultimately works as neither a self-aware black comedy nor a poignant exploration of the not-at-all-funny traumas it uncovers.

Pablo Schreiber, left, and Jon Bernthal in His & Hers Netflix

The first episode is all fake-outs and reveals too gratuitous to refrain from spoiling here (but consider this your warning). Thompson’s Anna Andrews initially appears as a frantic figure in a ratty hoodie, chugging wine from the bottle and rustling around an Atlanta apartment that is in an alarming state of disarray. But she quickly cleans up, saunters into the offices of a local TV news station, and finds that the anchor job from which she has taken a long leave of absence has been permanently handed to a smirking blonde named Lexy Jones (Rebecca Rittenhouse). An hour and change outside the city, in the picturesque town of Dahlonega, Bernthal’s Jack Harper is a police detective alerted by his young partner (Sunita Mani) that a body has been found in the forest. We know we’re supposed to like Jack because the first time we see him, he’s playing with an adorable tot (Ellie Rose Sawyer) whose mom, Zoe (Marin Ireland), is too hungover to parent. It is Anna’s insistence that her old boss let her report on the murder Jack is investigating that brings the leads together.