  Magnetoelastic properties of the spin-1/2 Ising-Heisenberg model on doubly
decorated planar lattices partially amenable to lattice vibrations are examined
within the framework of the harmonic approximation and decoration-iteration
transformation. It is shown that the mutual interplay between quantum spin
fluctuations and local fluctuations of lattice spacings enhances typical
quantum features like the quantum reduction of the magnetization in the ground
state of the quantum antiferromagnetic phase, while it does not affect the
ground-state behaviour of the classical ferromagnetic phase by no means. It
also turns out that local fluctuations of lattice spacings are responsible for
a much more pronounced reduction of the critical temperature in the quantum
antiferromagnetic phase than in the classical ferromagnetic phase.
