Finely layered porous structures are of practical interest in geophysics. Thin layers in such structures are described by an isotropic Biot model. Backus averaging on stratified poroelastic medium has been generalized and it has been found that effective long-wave equivalent medium in this case is a Biot model with tensor densities, which is called a generalized Biot model. This means that total and fluid densities are different along and across lamination. Only if the fluid density is the same is the effective model an ordinary transversally isotropic Biot model. Total density is a tensor even in the case when the layers differ only by fluid properties. Solid and fluid layers are included in consideration as partial cases for a Biot model. Wavefronts (group velocities) are found and demonstrated for some typical cases. When one of the layers is elastic, it may be considered as a porous Biot layer with infinite tortuosity. In this case the effective model has a triangular wavefront of second longitudinal waves which has zero velocity across lamination. When one of the layers is fluid, then the effective model is a generalized transversally isotropic Biot model, which is quite similar to the effective model of a medium of alternating solid and fluid layers.