  We report on the controlled switching of domain wall (DW) magnetization in
aligned stripe domain structures, stabilized in [Co (0.44 nm)/Pt (0.7 nm)]$_X$
($X = 48$, 100, 150) multilayers with perpendicular magnetic anisotropy. The
switching process, induced by an external magnetic field, is monitored by
measuring the evolution of the in-plane magnetization. % We show that the
remanent in-plane magnetization originates from the polarization of the
Bloch-type DWs. With micromagnetic simulations, we reveal that the reversal of
the DW polarization is the result of the emergence and collapse of horizontal
Bloch lines within the DWs at particular strengths of the external magnetic
field, applied opposite to the DW polarization. Our findings are relevant for
DW-based magnonics and bubble skyrmion applications in magnetic multilayers.
