We present an individual-based model describing disk-like self-propelled particles moving
inside parallel planes. The disk directions of motion follow alignment rules inside
each layer. Additionally, the disks are subject to interactions with those of the neighboring
layers arising from volume exclusion constraints. These interactions affect the disk
inclinations with respect to the plane of motion. We formally derive a macroscopic model
composed of planar self-organized hydrodynamic (SOH) models describing the transport
of mass and evolution of mean direction of motion of the disks in each plane, supplemented
with transport equations for the mean disk inclination. These planar models
are coupled due to the interactions with the neighboring planes. Numerical comparisons
between the individual-based and macroscopic models are carried out. These models
could be applicable, for instance, to describe sperm-cell collective dynamics.