We investigate the dipolar-exchange spin wave spectrum in thin ferromagnetic bilayers with in-plane magnetization, incorporating interlayer exchange coupling and intra- and interlayer dipolar interactions. In the continuum approximation, we analyze the nonreciprocity of propagating magnetic stray fields emitted by spin waves as a function of the relative orientation of the layer magnetizations that are observable by magnetometry of synthetic antiferromagnets or weakly coupled type-A van der Waals antiferromagnetic bilayers as a function of an applied magnetic field.