Monosilicides of 3d metals frequently show a chiral magnetic ordering with the absolute configuration defined by the chirality of the crystal structure and the sign of the Dzyaloshinskii-Moriya interaction (DMI). Structural and magnetic chiralities are probed here for Fe1-xCoxSi series and their mutual relationship is found to be dependent on the chemical composition. The chirality of crystal structure was previously shown to be governed by crystal growth, and the value of the DMI is nearly the same for all monosilicides of Fe, Co, and Mn. Our findings indicate that the sign of the DMI in Fe1-xCoxSi is controlled by the Co composition x. We have been able to directly measure the change of the link between structure and magnetism in this helimagnetic B20 alloy.