We show that asymmetries in total intensity and linear polarization between the radio jets and counter-jets in two lobed Fanaroff–Riley Class I (FR I) radio galaxies, B2 0206+35 (UGC 1651) and B2 0755+37 (NGC 2484), can be accounted for if these jets are intrinsically symmetrical, with decelerating relativistic outflows surrounded by mildly relativistic backflows. Our interpretation is motivated by sensitive, well-resolved Very Large Array imaging, which shows that both jets in both sources have a two-component structure transverse to their axes. Close to the jet axis, a centrally darkened counter-jet lies opposite to a centrally brightened jet, but both are surrounded by broader collimated emission that is brighter on the counter-jet side. We have adapted our previous models of FR I jets as relativistic outflows to include an added component of symmetric backflow. We find that the observed radio emission, after subtracting contributions from the extended lobes, is well described by models in which decelerating outflows with parameters similar to those derived for jets in plumed FR I sources are surrounded by backflows containing predominantly toroidal magnetic fields. These return to within a few kpc of the galaxies with velocities ≈0.25c and radiate with a synchrotron spectral index α≈ 0.55. We discuss whether such backflow is to be expected in lobed FR I sources and suggest ways in which our hypothesis can be tested by further observations.