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The word 'half-jokingly' is correct and can be used in written English.
It is typically used to describe a statement or action that is said or done in a joking manner, but still has some level of seriousness behind it. Example: "I half-jokingly told my boss that I would quit if I had to work overtime every day, but deep down I was hoping she would take my request seriously."
Exact(56)
"We like that," he said half-jokingly.
"Another housing bubble," he said, only half-jokingly.
Since then, I've called myself half-Mexican — only half-jokingly.
"Sell the house and move," he said, only half-jokingly.
(Foord half-jokingly but not inaccurately calls it "Feces Slip").
"Don't worry," one of my teachers told me half-jokingly.
Together, Howard explained only half-jokingly, the team is special.
We called it, half-jokingly, our Iran-Iraq friendship dinner.
"This is my kingdom," says Pierre, only half-jokingly.
He half-jokingly calls his predilection a sickness.
"I've always been thinnish," Munro insists, only half-jokingly.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com