Aims. We investigate the dynamics of the nebula around the symbiotic star Hen 2-147, determine its expansion parallax, and compare it with the distance obtained via the period-luminosity relation for its Mira variable. Methods. A combination of multi-epoch HST images and VLT integral field high-resolution spectroscopy is used to study the nebular dynamics both along the line of sight and in the plane of the sky. These observations allow us to build a 3D spatio-kinematical model of the nebula, which, together with the measurement of its apparent expansion in the plane of the sky over a period of 3 years, provides the expansion parallax for the nebula. Additionally, SAAO near-infrared photometry obtained over 25 years is used to determine the Mira pulsation period and derive an independent distance estimation via the period-luminosity relationship for Mira variables. Results. The geometry of the nebula is found to be that of a knotty annulus of ionized gas inclined to the plane of sky and expanding with a velocity of similar to 90 km s(-1). A straightforward application of the expansion parallax method provides a distance of 1.5 +/- 0.4 kpc, which is a factor of two lower than the distance of 3.0 +/- 0.4 kpc obtained from the period-luminosity relationship for the Mira (which has a pulsation period of 373 days). The discrepancy is removed if, instead of expanding matter, we are observing the expansion of a shock front in the plane of the sky. This shock interpretation is further supported by the broadening of the nebular emission lines.