Last night's viewing: Hit & Miss, Sky Atlantic; My Big Fat Fetish, Channel 4

You can tell that Hit & Miss is going to be a cut above from what it chooses to surprise you with. The central character, Mia, is a hired killer. She’s not the first female assassin we’ve seen on screen by a long shot, but this combination of gender and profession is still unusual enough that a more conventional series might tease you with the reveal. We’d see Mia touching up her lipstick first, say, and be allowed to coast with our preconceptions for a while before she stepped out of the car and shot her first victim. Here, it happens the other way around.

Mia isn’t an ordinary woman, though, as we discover when she strips for the shower just a little later. What’s inside her bra is what you might expect. What’s inside her pants is not: Mia has a penis. But this moment too is studiedly matter of fact. Hettie Macdonald frames the revelation as if we’ve noticed but the camera hasn’t – because it isn’t that big a deal. The real surprise, the one that makes Mia herself reel and blink back the tears is the discovery that she’s a father. Or a mother. Or some hybrid of the two that has yet to be worked out.

Along with her payment for that first clinical execution, Mia gets a forwarded letter from Wendy, a women she’d loved when she was still a man. Wendy is dying of cancer and the letter consigns her children to Mia’s care, including a young boy called Ryan, who is Mia’s biological son. And from that moment what Mia does to earn a living is peripheral to the charged drama of her domestic mission (which, crucially, is the kind of mission a lot of viewers are on too). It isn’t going to be easy. The family Mia finds living up on the moors above Manchester is as ramshackle as their smallholding. They are looked after by the aggressively defensive Riley, the oldest sister and a girl made furious by grief. She resents Mia’s intrusion and is determined to push her out again.

Paul Abbott and Sean Conway’s script is mostly terse and understated, with the occasional flash of romantic colour. One of the most poignant moments, when Ryan learns that Mia had never been told about his existence, is conveyed in just two syllables: “Why not?” he says, a line that is beautifully delivered by Jorden Bennie. Later, though, when Ryan shares with Mia his fear that things are going to change, she reassures him by explaining that without change we would never have butterflies, a line that trembles on the edge of mawkish.

Chloë Sevigny’s performance here may remind some older viewers of Stanley Baxter; there’s something about the combination of exaggerated femininity and dead-pan solemnity that recalls his essays in drag. But given the plot it works, and (having seen episode two) it’s an armour that’s going to peel open. What really charges the drama, though, is the uncertainty about what gender you might assign to Mia’s virtues and vices. When she savagely beats the local bully who’s called for the rent and teaches Ryan to box, is she substituting for a missing father or mother? And when she asks her handler whether the next target has any children, what has been woken in her – a paternal instinct or a maternal one?

There’s a sense that all gender relations have been twisted out of true – into exploitation or violence – and that only the love and security of a family, however odd it is, can put things right. It’s wonderfully unexpected and unpredictable and a debut commission in original drama that Sky Atlantic has every reason to be proud of.

Which is more than you can say for My Big Fat Fetish, a tawdry documentary about subscription websites catering for those with a penchant for obese women. Channel 4 should know better but simply couldn’t stop itself gawping.