  We study angular-momentum couplings in $^{87}$Rb$_2$ Rydberg molecules formed
between Rydberg and 5S$_{1/2}$ ground-state atoms. We use a Fermi model that
includes S-wave and P-wave singlet and triplet scattering of the Rydberg
electron with the 5S$_{1/2}$ atom, along with the fine structure coupling of
the Rydberg atom and hyperfine structure coupling of the 5S$_{1/2}$ atom. We
discuss the effects of these couplings on the adiabatic molecular potentials.
We obtain bound-state energies, lifetimes, and electric and magnetic dipole
moments for the vibrational ground states of the $^{87}$Rb$(n$D$+5$S$_{1/2})$
molecules in all adiabatic potentials, with fine and hyperfine structure
included. We also study the effect of the hyperfine structure on the deep
$^3$S-wave- and $^3$P-wave-dominated adiabatic molecular potentials, which
support high-$\ell$ $^{87}$Rb$_2$ Rydberg molecules.
