Joint signal representations of arbitrary variables extend the scope of joint time-frequency representations, and provide a useful description for a wide variety of nonstationary signal characteristics. Cohen's marginal-based theory for bilinear representations is canonical from a distributional viewpoint, whereas, from other perspectives, such as characterization of the effect of unitary signal transformations of interest, a covariance-based formulation is needed and more attractive. In this paper, we present a simple covariance-based characterization of bilinear joint signal representations of arbitrary variables. The formulation is highlighted by its simple structure and interpretation, and naturally extends the concept of the corresponding linear representations.