  Context. Complex bipolar shapes can be generated either as a planetary nebula
or a symbiotic system. The origin of the material ionised by the white dwarf is
very different in these two scenarios, and it complicates the understanding of
the morphologies of planetary nebulae. Aims. The physical properties,
structure, and dynamics of the bipolar nebulae, M 2-9, Mz 3, and Hen 2-104, are
investigated in detail with the aim of understanding their nature, shaping
mechanisms, and evolutionary history. Methods. Long-slit optical echelle
spectra are used to investigate the morpho-kinematics of M 2-9, Mz 3, and Hen
2-104. Near-infrared (NIR) data, as well as optical, spectra are used to
separate Galactic symbiotic-type nebulae from genuine planetary nebulae by
means of a 2MASS J-H/H-Ks diagram and a {\lambda}4363/H{\gamma} vs.
{\lambda}5007/H\b{eta} diagnostic diagram, respectively. Results. The
best-fitted 3-D models for M 2-9, Mz 3, and Hen 2-104 provide invaluable
kinematical information on the expansion velocity of its nebular components by
means of synthetic spectra. Kinematical ages of the different structures of M
2-9 and Mz 3 have also been determined. Both diagnostic diagrams show M 2-9 and
Hen 2-104 to fall well within the category of having a symbiotic source,
whereas Mz 3 borders the region of symbiotic and young planetary nebulae in the
optical diagram. The optical diagnostic diagram is shown to successfully
separate the two types of nebulae. Conclusions. The morphology, kinematics, and
evolutionary history of M 2-9, Mz 3, and Hen 2-104 are better understood using
the interactive 3-D modelling tool shape. The optical and NIR diagnostic
diagrams used are important techniques for separating Galactic symbiotic-type
nebulae from genuine planetary nebulae.
