We propose new covariance functions for bivariate Gaussian random fields that are very general and include as special cases other popular models proposed in earlier literature, namely, the bivariate Matern and bivariate Cauchy models. The proposed model allows the covariance margins to belong to different parametric families with. To our knowledge, this is the first model of this type to be proposed in the literature. For instance, one of the margins can be of the Matern type, whereas the latter can index long-range dependence. Estimation of the model is illustrated through simulation.