According to nLab:

> If \$$\mathcal{C}\$$ is a 2-category, there is its double category of squares \$$\mathrm{Sq}(\mathcal{C})\$$ whose objects are those of \$$\mathcal{C}\$$, both of whose types of morphisms are the morphisms in \$$\mathcal{C}\$$, and whose squares are 2-morphisms in \$$\mathcal{C}\$$ with their source and target both decomposed as a composite of two morphisms. (These squares are sometimes called *quintets* \$$(\alpha,f,g,h,k)\$$ where \$$\alpha\colon f g \to h k\$$, and so this double category is said to be a quintet construction.)

so it sounds like any bicategory is a special case of a double category.