Using spin-polarized low energy electron microscopy, we discovered a new type of domain wall structure in perpendicularly magnetized Fe/Ni bilayers grown epitaxially on Cu(100). Specifically, we observed unexpected Néel-type walls with fixed chirality in the magnetic stripe phase. Furthermore, we find that the chirality of the domain walls is determined by the film growth order with the chirality being right handed in Fe/Ni bilayers and left handed in Ni/Fe bilayers, suggesting that the underlying mechanism is the Dzyaloshinskii-Moriya interaction at the film interfaces. Our observations may open a new route to control chiral spin structures using interfacial engineering in transition metal heterostructures.