jest.setup.js

const { equals } = require('expect/build/jasmineUtils');

expect.extend({
  toContainObject(received, argument) {
    const pass = (() => {
      if (Array.isArray(argument)) {
        return equals(received, 
          expect.arrayContaining(argument.map(arg => expect.objectContaining(arg)))
        );
      }
      return equals(received, 
        expect.arrayContaining([
          expect.objectContaining(argument)
        ])
      );
    })();
    if (pass) {
      return {
        message: () => (`expected ${this.utils.printReceived(received)} not to contain object ${this.utils.printExpected(argument)}`),
        pass: true
      }
    } else {
      return {
        message: () => (`expected ${this.utils.printReceived(received)} to contain object ${this.utils.printExpected(argument)}`),
        pass: false
      }
    }
  }
});

example usage on a first level and nested object: (should pass)

expect([{
  foo: 'bar',
  prop1: 'what',
  prop2: [{
    xyz: 'asd',
    bar: 'foo',
  }],
}]).toContainObject([{
            foo: 'bar'
            prop2: expect.toContainObject({
                bar: 'foo',
            }),
        },{
          foo: 'bar'
            prop2: expect.toContainObject({
                xyz: 'asd',
            }),
        }]);