Based on the manga Mamonogatari Itoshi no Betty created by Koike Kazuo and Kanou Seisaku.
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Betty, a devil-girl with the face of an angel and a heart of gold, falls in love with a human gangster, Danpei Kimogawa, when they meet during a rainstorm. They end up living together in Tokyo - though Danpei has trouble coping with his new in-laws, a witch and a demon, who like dropping by at inappropriate moments. 
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Betty has actually been sent to the human world on a mission to defeat the demon Lutan. While Betty continues her task, her skeletal grandmother sends nubile nymphs to tempt Danpei and see if he is suitable husband material.

Itoshi no Betty Mamonogatari