This could be "Humanoid Monster Bem" (Yōkai Ningen Bemu), an anime first aired in 1968.
The main characters are three mysterious creatures, named Bem, Bera and Bero, respectively looking as a dark-skinned tall man with a black coat and hat and a white cane, a pale woman wearing a purple dress and a green/red cape, and a kid dressed in red.
In this form they appear mostly human (despite having only three-fingered hands) and interact with other people, but they can switch to a more monstrous form.
Here are the characters in their humanoid and monstrous forms (these images are from the 2007 remake series, but the design is quite the same as in the original one):
Their origins are only hinted at. An introduction repeated at the beginning of each episode after the opening song states that "no one really knows when they were born; in a dark and silent place a cell multiplied, giving origin to three living beings, different from humans and from any other life form on Earth; behind their hideous appearance, they have a deep sense of justice".
Each episode tipically has them arriving in a new location and investigating the sinister events happening there, involving either supernatural monsters or cruel criminals.
The specific episode you remember should be episode #18 "The mysterious sculptor".
A mad artist creates his statues by capturing people and encasing them in bronze or plaster. After discovering the corpse inside one of these statues, Bero and the other monsters try to stop him.