  Under tidal forcing, icy satellites with subsurface oceans deform as if the
surface were a membrane stretched around a fluid layer. `Membrane worlds' is
thus a fitting name for these bodies and membrane theory provides the perfect
toolbox to predict tidal effects. I describe here a new membrane approach to
tidal perturbations based on the general theory of viscoelastic-gravitational
deformations of spherically symmetric bodies. The massive membrane approach
leads to explicit formulas for viscoelastic tidal Love numbers which are exact
in the limit of zero crust thickness. Formulas for load Love numbers come as a
bonus. The accuracy on $k_2$ and $h_2$ is better than one percent if the crust
thickness is less than five percents of the surface radius, which is probably
the case for Europa and Titan. The new approach allows for density differences
between crust and ocean and correctly includes crust compressibility. This last
feature makes it more accurate than the incompressible propagator matrix
method. Membrane formulas factorize shallow and deep interior contributions,
the latter affecting Love numbers mainly through density stratification. I show
that a screening effect explains why ocean stratification typically increases
Love numbers instead of reducing them. For Titan, a thin and dense liquid layer
at the bottom of a light ocean can raise $k_2$ by more than ten percents. The
membrane approach can also deal with dynamical tides in a non-rotating body. I
show that a dynamical resonance significantly decreases the tilt factor and may
thus lead to underestimating Europa's crust thickness. Finally, the dynamical
resonance increases tidal deformations and tidal heating in the crust if the
ocean thickness is of the order of a few hundred meters.
